







Exponential form 
20170706 

From estela: what is exponential form of 9×1000 Answered by Penny Nom. 





Exponential form 
20170304 

From michael: I was teaching my student about exponent when we stumbled across this problem.
"write (125)^3 in exponent form"
The problem is with the number "125". I think 125 = (5)^3. But one of my student thought that it is 125= 5^3.
Both of them is equal to 125 but they totally different in structure. I wonder which one is correct and why it is. I am worried if they get this wrong, it might spell problem in the future when we start substituting the numbers with variable.
Thank you very much for reading my question and answering it. Answered by Penny Nom. 





Exponential form 
20160831 

From Lily: Hi! I was wondering, I was having a little issue understanding this one problem. It was "write 81 in exponential 2 different ways" and I already got 9(2) but I was wondering what the second one could be! Thanks! Lily Answered by Penny Nom. 





Exponential form 
20160126 

From Jufe: What is the exponential form of ³√11x² Answered by Penny Nom. 





Exponential growth 
20160126 

From Paul: The value of a stamp was 0.03 in 1851. The value in 2011 is $50,000. If the value increased exponentially, what is the annual growth rate? Answered by Penny Nom. 





Exponential form 
20151017 

From Will: What is exponential form of 8? Answered by Penny Nom. 





Exponential notation 
20141127 

From Jaqui: May sound super easy, but how would you SHOW that you simplified
3x3 to the power of 2 (the little 2)?
thank you!
Jaqui Answered by Penny Nom. 





Prime factorization in exponent form 
20141031 

From Emma: I need to find out how to make a prime factorization of 120 in exponential form. Answered by Penny Nom. 





What is the exponential form of 1/square root of 6v? 
20140216 

From Prince: What is the exponential form of 1/square root of 6v Answered by Penny Nom. 





Prime factorization 
20140206 

From Kadeejah: Write the prime factorization of 37 in exponential form Answered by Penny Nom. 





Exponential form 
20131201 

From Alina: My question says to express each number in exponent form in as many different ways as I can; 16, 81 and 64. How do I do this? Answered by Penny Nom. 





How do i write log_8(P) =7 in exponential form? 
20130414 

From nancy: How do i write this in exponential form log8P =7 Answered by Penny Nom. 





Exponential form 
20130205 

From Sandra: What is 37,008 in exponential form? Help me please!!! Answered by Penny Nom. 





What's your secret? 
20121111 

From ryan: Tuscan school has a fair. At the fair, Pia plays "what's your secret?
The game starts with 3 players who are told the same secret.
Each of those 3 players tells another 3 player, and so on.
At the end of the 3rd round, everyone who knows the secret
will compare what they have heard. What number in exponent form
represents the number of people who know the secret after 3 rounds?
How many people is that?
Thank you very much.
P.S. I got 3 cube. which is 27
But when i map it out I end up with 39. Answered by Penny Nom. 





Exponential form 
20120904 

From angie: How do i write 9^5 in exponential form? Answered by Penny Nom. 





Exponntial form 
20120830 

From Robin: My math teacher has asked the question:
"Write mmmxxjmyy2 in exponential form"
How would you solve this problem? Answered by Penny Nom. 





The exponential function form f(x)=a^x 
20120813 

From Lucy: Hi,
Why does the "a" value in the exponential function form f(x)=a^x have to be negative? Answered by Penny Nom. 





Expanded exponential form? 
20120612 

From Ramon: express the numbers 990 614 000 005 in expanded exponential form. Answered by Harley Weston. 





The spread of a rumor 
20120409 

From Roohi: The function f(t) = a/(1+3e^(bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents. Answered by Penny Nom. 





Radioactive decay 
20120402 

From Christy: Hello, how do I go about answering this question?
Should I be using the formula Ce^(kt)?
Given that the decay constant for Radium is .000428/year, how long, to the nearest year, does it take a sample to decay to 15% of its present mass? Answered by Penny Nom. 





Exponential form 
20120115 

From Helen: How do you write (1/x) in exponential form? Answered by Penny Nom. 





Exponential form 
20111212 

From Zoey: What is the exponential form of 1/8?? Answered by Penny Nom. 





I started with Euler's identity and manipulated it 
20111114 

From anonymous: I started with Euler's identity and manipulated it
e^i*pi=1
e^i*pi=(1)^1
e^i*pi=1
e^i*i*pi=(1)^i
e^pi=(1)^i
e^pi=(1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(1)^i=0.0432139183... What did I do wrong? Answered by Robert Dawson. 





A log equation in exponential form 
20111111 

From Sarah: Express the equation in Exponential form
log2 to the 16th power=4 Answered by Penny Nom. 





Exponential form? 
20110830 

From Emily: I have a 6th grader that needs to find out what is the exponential form of 461,885,811 Answered by Penny Nom. 





Exponential form 
20110823 

From kiara: The African bush elephant is the largest land animal and
weighs about 8 tons . Write the amount in exponential form . Answered by Robert Dawson. 





Exponential form 
20110518 

From Kara: How do I write this in exponential form?
log 1/8 = 3 Answered by Penny Nom. 





(7cubed * 8(exponent6))exponent 6 
20110129 

From Shalaine: What is the exponential form of (7cubed•8(exponent6))exponent 6? Answered by Penny Nom. 





Exponential form 
20110102 

From jumana: find any five examples of exponential form from real life situation Answered by Penny Nom. 





Powers 
20101020 

From dylan: how do you write 20736 in exponential form .same for 1728 and 50625.
is there a formula to figure out how to express large know numbers in exponential form. Answered by Penny Nom. 





An exponential equation 
20101019 

From Sandi:
Question from sandi, a student:
I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it.
Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed.
Time (in days)Population
0500
1600
2720
3864
41037
51244
61493
71792
82150
1.)Using graphing calculator make a scatter plot of the data in table.
I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1
2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this.
3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days. Answered by Penny Nom. 





Exponential form 
20101006 

From celina: what is the exponential form of 4x*4x Answered by Penny Nom. 





Exponential form 
20100824 

From Courtney: What the Exponential form? For Ex. X2*X5*X4?? Answered by Penny Nom. 





Exponential form 
20100616 

From charlotte: what is the exponential form of 6x6x6x5x5x5x5= Answered by Robert Dawson. 





graph y=(2x^23x)e^ax 
20100531 

From James: graph y=(2x^23x)e^ax Answered by Robert Dawson. 





Exponential form 
20090918 

From karen: Q: Write the following in exponent from: a * a * a * a * * * a, where there are n 1 a's
note: *asterisk means times. Answered by Penny Nom. 





Exponential form 
20090908 

From hanna: hi,
well i am really bad in math and i have a math paper and i was just
wondering what 3x3x3x3x3 was in exponential form and what is
exponential in a way a person like me would understand? Answered by Penny Nom. 





What is 8 tons in exponential form? 
20090901 

From Tyler: what is 8 tons in exponential form Answered by Penny Nom. 





Exponential form 
20090831 

From cecil: what is the exponent form 564000? Answered by Stephen La Rocque and Harley Weston. 





Fitting the curve y=a*exp(b*x)+c 
20090812 

From aika: Could one show me the complete algorithm and formula for finding the coefficients (a,b, and c) in exponential regression model
y=a*exp(b*x)+c Answered by Robert Dawson. 





Exponential form 
20090805 

From motaz: Let x = log_2 1/8 Write the exponential form of the equation and solve the equation for x Answered by Stephen La Rocque. 





Exponential form 
20090416 

From Pete: Hi,
How do you express ³√h^4 in exponential form. I am having a lot of
trouble with this one.
thanks
Pete Answered by Stephen La Rocque. 





Grain of rice on a chess board 
20090330 

From andy: Is there an easy way for my students to find out 8 to the power of 21 to solve the grains of rice doubling investigation on a chessboard? Any suggestions welcome. Thanks very much Answered by Robert Dawson and Claude Tardif. 





What is i^i? 
20081227 

From randomness: i have learnt that 'i' is square root of 1. What is then i^i ? It baffles my maths teacher... Answered by Robert Dawson and Penny Nom. 





Exponential form 
20081021 

From layla: how we wite 256 in exponential form Answered by Harley Weston. 





Logs and exponentials 
20081006 

From Charles: I seem to remember you could solve exponential problems using natural logs quite simply without calculators, such as the fifth root of 400 or 33 to the 4th power. All you did was convert the number to its natural log and then just divide by 5 or multiply by 4 and then convert it back. I just remember how to do this. Thanks. Answered by Harley Weston. 





Exponential form 
20080925 

From Pat: The African bush elephant is the largest land animal and weighs about 8 tons. Write this amount in exponential form. Answered by Penny Nom. 





Exponential form 
20080916 

From shawn: Write the product in exponential form: 5.5.5.2 Answered by Penny Nom. 





What is the derivative of (2^sinx)/(logbase4(2x+1))? 
20080916 

From Jesse: What is the derivative of (2^sinx)/(logbase4(2x+1)) Answered by Harley Weston. 





Solving Exponential Equations Using Logarithms 
20080915 

From Todd: 7(6^x)=6e^2x Answered by Janice Cotcher. 





1,679,616 as a power of 6 
20080903 

From Denise: express 1,679,616 in exponential form as a power of 6. Answered by Penny Nom. 





Solve e^x + e^(x+1) = 250 
20080825 

From Laura: "solve this equation correct to three decimals"
e^x + e^x+1= 250 Answered by Penny Nom. 





Right Sided Limit of an Exponential Function 
20080729 

From joseph: I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x
which look like this lim x^sinx
x>0+ Answered by Harley Weston. 





Exponential form 
20080703 

From Kent: How to write 8 365 005 106 in expanded and exponential form? May I request you also to explane how does it solve. Answered by Stephen La Rocque. 





Write log_2 (1/8) = 3 in exponential form 
20080627 

From Jaime: how do you write log2 (1/8) = 3 in exponential form?
the 1/8 is a fraction and the 2 is a base of 2 Answered by Penny Nom. 





The cube of 2y in exponential form 
20080519 

From Xiu: I dont get this question..
Write "the cube of 2y" in exponential form. I know the answer is (2y)^2 but i really don't understand why. Can you explain how to do this whole problem for me? Answered by Leeanne Boehm. 





The inverse of a function 
20080503 

From keith: please help me find the inverse of this function:
h(t) = 2 + 4 ln(15t) Answered by Stephen La Rocque. 





The exponential form of x radical y to the third power 
20080330 

From Jennifer: what is the exponential for of x radical y to the third power Answered by Penny Nom. 





Exponential form 
20080216 

From annna: i already got the answer for what is the prime factorization of 648 which is 2x2x2x3x3x3x3
but how do i write that answer in exponential form? Answered by Penny Nom. 





Growth factor and growth rate 
20080213 

From william: what is the difference between growth factor and growth rate? Answered by Stephen La Rocque and Harley Weston. 





How do I write the following in exponential form? 
20080109 

From Mandy: How do I write the following in exponential form?
( square root of a^2 b)^5 Answered by Penny Nom. 





Exponential form 
20080108 

From liam: i was wondering if anyone could help me with this question and tell me how and what the did; exponetial form of 4 326 180 501 Answered by Stephen La Rocque. 





Multiplying exponentials 
20080102 

From jessie: Can you please explain how to put x^3 y^2 times x^1 y^3 in simplest exponential form? Answered by Penny Nom. 





Radicals in exponential form 
20080102 

From Andre: The title of the section in my textbook is to write each of the following
radicals in exponential form.
My question is how do u write the squareroot of 10 in exponential form? Answered by Penny Nom. 





Exponential form 
20071130 

From Sasha: How do I write the number 127398 in exponential for? Answered by Penny Nom. 





Exponential Growth 
20071119 

From lisa: Hi i am a 8th grader who is learning about algebra
and we are having test on exponent and i don't really get it
i asked my teacher and she told me i should pay more attention
so i want to know what exponential Growth means Answered by Penny Nom. 





Exponential form 
20071116 

From ashley: write a sentence for exponential form. Answered by Penny Nom. 





Doubling every day 
20071007 

From Jerrie: Patti saved pennies for 10 days. The first day she saved 1 cent. Every day after that she saved twice as much as the day before. How much money did Patti save altogether? Answered by Stephen La Rocque. 





Exponents 
20070926 

From Calvin: Exponential form
5 3exponent x 5 4exponent divide 5 2exponent Answered by Stephen La Rocque. 





Exponential regression 
20070924 

From Anonymous: I need help in finding this. Find a formula for exponential regression.
Determine how to calculate a and b in the formula.
Y = ba^x
where y is as a function of x. Answered by Penny Nom. 





Exponential form 
20070912 

From Ericha: How do I express 1,679,616 in exponential form as a power of 6 using a calculator? Answered by Stepehe La Rocque and Penny Nom. 





Prime factors in exponential form 
20070906 

From Michelle: how would you write this: factor 48 as a product of primes written in exponential form Answered by Stephen La Rocque. 





Exponential form 
20070905 

From jeanette: the African bush elephant is the largest animal and weighs 8 tons. write this amount in exponential form. Answered by Stephen la Rocque and Penny Nom. 





Exponential form 
20070831 

From Victoria: The cost of each space shuttle is about $10,000,000.
Write this amount in exponential form. Answered by Stephen La Rocque. 





Exponential form 
20070829 

From Emily: Write the Exponential Form of 125 x 25 and 81 x 27. Answered by Stephen La Rocque. 





Exponential form: x^y 
20070622 

From Kishor: whats the easy way to calculate X raised to Y where y is much greater than x. Answered by Stephen La Rocque. 





Understanding log equations 
20070510 

From Sean: The number, N, of people who have heard a rumor spread by mass media at time, t, in days is modelled by N (t) = a / 1+ be^ kt. If 50 people have heard the rumour initially and 300,000 people hear the rumour eventually, find a and b. If the rumour is initially spreading at the rate of 500 people per day, find k. Answered by Penny Nom. 





Exponential form 
20070416 

From Cassia: I was just wondering, how do you write the squared root of 7x(to the 5th) in
exponential form? If you could help explain that I'd be grateful. Thanks Answered by Brennan Yaremko. 





exponential decay of Carbon14 
20070312 

From Christine: How do I set up the exponential decay formula for Carbon 14 with an initial amount of 1500 grams. Answered by Stephen La Rocque. 





Exponential form of complex numbers 
20070212 

From Austin: When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is 1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks Answered by Penny Nom. 





After how many hours will the class have been notified? 
20061110 

From Brittany: A college math class consists of 32 students. On Monday at 9:00 a.m., the teacher tells one student to notify other students that the test scheduled for Wednesday at 9:00 a.m. has been cancelled. The model for the number of students in the class who will have heard this information after t hours is N=3232e^0.02t. After how many hours will the class have been notified? Answered by Stephen La Rocque. 





Putting things in exponent form 
20061018 

From Sheila: Write in exponential form 2 sq. root a with an exponent 5. I do not understand on how to do it. Answered by Stephen La Rocque. 





Geometric sequence and basic functions (graphs) 
20060420 

From Marlene: Which of the basic functions is related to the geometric sequence:
Linear, Quadratic, Rational, or Exponential?
Can you give me an example of how it would be used in normal life? Answered by Stephen La Rocque. 





An exponential function 
20060403 

From Meadow: The graph of an exponential function passes through the points (0,1) and (4,10) find the constant of growth or decay. State the function. Answered by Stephen La Rocque. 





Exponential decay 
20060329 

From Casey: Fifty milligrams of a drug was injected into a patient at 6am. The drug is known to be eliminated according to the law of exponential decay. At 8.30am it was determined that 60% of the drug remained in the body. How many milligrams will remain in the body at midday? Answered by Penny Nom. 





Express t as a function of d 
20051130 

From Matthew:
I have a problem on my homework I cant seem to figure out. Basically it gives me this Linear Regression Equation:
ln t=1.5 ln d0.8954
and it wants be to transform the equation expressing t as a function of d. For some reason I keep getting it wrong. Anyone got an idea of how to do this?
Answered by Penny Nom. 





2^10 = 1/2^x  1 
20041213 

From Randy: Could you explain to me how the following equation is solved please.
2^10 = 1/2^x  1 Answered by Harley Weston. 





e = ln(b/a) solve for a 
20041201 

From Daniel: I am trying to make "a" the subject of this equation "e = ln(b/a)" but am not sure if i'm doing it right. Any help would be appriciated, Answered by Claude Tardif. 





x = 2^x 
20040712 

From A student: If the graphs of y=x and y=2^{x} are drawn on the same set of axes, they will intersect when x is equal to what?
(1)1
(2)2
(3)0
(4)They won't intersect.
I know the answer is number 4 by graphing which is permitted; however, I would like to know if there is any algebraic way to do this type of problem.If yes, please show me how.Thanks. Answered by Penny Nom. 





A sequence that converges to e 
20030316 

From Dane: Something I noticed fooling around with a calculator about 30 years ago. Considering e = 2.718281828459045.... Using Window's Calculator you will find 1.1^{11} = 2.8531167... 1.01^{101} = 2.731861... 1.001^{1001} = 2.71964085... 1.0001^{10001} = 2.71841774... 1.00001^{100001} = 2.7182954... 1.000001^{1000001}1 = 2.178231875... 1.0000001^{10000001} = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'1^{1'infinite number of zeros'1} = e. Answered by Penny Nom. 





Exponential notation 
20021019 

From Ivy: I understand how to figure out for example 4 to the power of 3,what I don't understand is how to figure it out using both negative numbers and negative exponents,as an exaple 4 to the power of 6 and what makes this different that (5) to the power of 7,please help me if you can.I am an adult taking correspondence and finding it quite frustrating. Answered by Penny Nom. 





Exponential form 
20011211 

From Crystal: Hi, I am asking a question on behalf of a homeschooling grade 11 student. She is having trouble with changing something like (3^{4})^{2} into a exponential form. First of all she needs to know what the term means "exponential form" and then the process of it. Answered by Penny Nom. 





Earthquake warning 
20010903 

From Dillon: In the city of Skangai there are 6 million people.Each person has to tell 2 more people that theres going to be an earthquake. After they do they leave the city. There will be no duplications.It takes 3 minutes to tell each person. How long will it take for the whole city to know about the earthquake? Answered by Penny Nom. 





Exponential form 
20010606 

From A student: Hello can u please answer my question what is the exponent form of 8x8x8x8 Answered by Penny Nom. 





Conservation, consumption and population growth 
20010604 

From Steve: I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 41990 to 33,871 in 42000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: . . . Answered by Penny Nom. 





Graphing F(x) = 3^{x} 
20001106 

From Jose: graph the exponential problem F(x)=3^{x} Answered by Harley Weston. 





Radioactive decay 
20000518 

From Catherine Sullivan: Please help me with the following: The radioactive isotope carbon14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to carbon12 at a rate proportional to the amount of C14 present, with a half life of 5730 years. Suppose C(t) is the amount of C14 at time t.  Find the value of the constant k in the differential equation: C'=kC
 In 1988 3 teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of C14 contained in freshly made cloth of the same material. How old is the Shroud according to the data?
Answered by Harley Weston. 





A colony of bacteria 
20000422 

From Nicci Demmin: Suppose that the bacteria in a colony can grow unchecked, by the law of exponential change. The colony starts with one bacterium and doubles every half hour. How many bacteria will the colony contain at the end of 50 hours? Answered by Penny Nom. 





y = x^x^x^x... 
20000405 

From Michael Hackman: Find the derivative of: y = x^x^x^x... on to infinity. Answered by Claude Tardif. 





Compounding continuously 
20000321 

From Gina: You deposit $1500 in an account that pays 6.5% annual interest, compounded continuously. Find the balance after 10 years. I'm not sure what to do with the "compounded continuously" part. Answered by Penny Nom. 





Functions that satisfy f' = f 
20000316 

From Kevin Palmer: Recently my calculus teacher asked his students to try and find any functions whose derivatives where the exact same as the original function. The only function then I have determined that statement to be accurate in is all the natural exponential functions. Ex. f(x) = e^{x}, f'(x) = e^{x} If possible could you please email me all the functions that you can find in which the original function and its derivative is identical. Answered by Claude Tardif. 





Log Cancel 
19991203 

From Justin Murray: Ok I feel like a goof because I know this and I cant think of an answer But I want to isolate the x in the function y=2^x how do I do this? Answered by Harley Weston. 





Zero to the zero 
19991202 

From A middle school teacher: I am a middle school teacher who is looking for a precise explanation of why zero raised to the zero power is undefined. I am hoping to get an explanation using something other than the fact that diividing by zero is undefined. Answered by Penny Nom. 





Get rich quick 
19991202 

From Holly Hutson: If one cent were placed in an investment that doubles in value every day, what would be the value of the investment at the end of 30 days? Answered by Penny Nom. 





A matching quiz 
19991120 

From William J. Ricciardi: I gave a matching quiz the other day and one of my students got all 9 incorrect. That got me thinking......What is the probability that someone could get all 9 questions incorrect? Answered by Peny Nom. 





Two derivatives 
19991116 

From Gina Renicker: The derivative of: y=e^{(xlnx)} and y=x^{2arctan(x1/2)} Answered by Harley Weston. 





2 to the x and x squared 
19990917 

From John: For what values of x is 2 to the exponent x greater than x squared? Answered by Harely Weston. 





Slopes of curved lines 
19990609 

From Stephen Ehrler: When one plots the graphs of y=2^{x}, y=3^{x}, y=x^{x} When each of these graphs pass through point (0,1) do they have the same slope? I know they are different lines but is it possable that they have the same slope at point (0,1). Answered by Harley Weston. 





Natural Logarithm Functions 
19970423 

From Rickson: The following two questions are some of my son's homework that he is having trouble with......any advice or assistance would be appreciated. (eX)5=1000.............the X and 5 are exponents lnx + ln(x+3) = ln10 In each question the problem is to find x. Answered by Harley Weston. 

