







How to find last two or three digits of a large exponent like 17^256? 
20170330 

From Raginee: How to find last two or three digits of a large exponent like 17^256? Answered by Penny Nom. 





Differentiate y = x^x^x 
20170319 

From Nafis: differentiate y = x^x^x Answered by Penny Nom. 





Powers 
20160929 

From Ezra: i cant figure out this question. Can you please help
ezra
product of power (6x4)3 Answered by Penny Nom. 





Order of operations 
20150912 

From Tanisha: I would just like to double check if something like 5x squared times 4x cubed equals 20x to the power of 5??
It's just that we were told you can only answer an equation like this if the base is the same...so does that mean the x part or the whole thing like 5x?
I'm sorry if that didn't make sense!
Thank you for your help!! 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. 





650*(1+0.005)^96 
20130417 

From joAnn: i am trying to figure out how to solve a question like this for example:
650(1+.005)96
I have been doing it this way but takes forever and wanted to know a shorter way
650 x 1.005 x 1.005 x 1.005 x 1.005 96 times
HELP Answered by Penny Nom. 





A cylinder is to be filled with peas. 
20120612 

From Silje: Hi! How can I solve the following question without the use of a calculator?
"A cylinder is to be filled with peas. It is done like this: At 12:00 o'clock you put 1 pea in, at 12:01 you put 2 peas in, at 12:02 you put 4 peas in, at 12:03 you put 8 peas in, and so on.
This continues until 14:00 o'clock (two hours later), when the last peas are put in and the cylinder is full. At what time is the cylinder half full?" Answered by Robert Dawson. 





81+8 to the 3 power 
20120308 

From KiMesha: 81+8 to the 3 power Answered by Penny Nom. 





Exponential form 
20111212 

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





A pattern is built with cubes. 
20110208 

From e: A pattern is built with cubes.
The first item is 1 cube.
The second item is a block of 8 cubes.
The third item is a block of 27 cubes.
If the pattern is continued, how many cubes are needed for the fourth and fifth? Answered by Penny Nom. 





[sec^2x]*[sec^2x] 
20101216 

From Hari: [sec^2x]*[sec^2x]=...? Answered by Penny Nom. 





Two algebraic expressions 
20101029 

From chaptay: what is the difference between x(n^2) and x(n)^2 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. 





(5xy)^5 
20100910 

From ana: (5xy)^5 Answered by Penny Nom. 





(x + a)^2 
20100604 

From a: If the 3rd , 4th, 5th terms in the expansion of (x + a)powe "n" are 720, 1080, 810 respectively, then
find the values of x, a and n. Answered by Penny Nom. 





0.999 ^ (500) 
20100307 

From debra: I just need to know how to solve the following problem without using a calculator: .999 ^ (500). I know the answer is .606, I just want to do it by hand since I can't use a calculator on my test. Answered by Penny Nom and Claude Tardif. 





Evaluating x^2 + (yz  3)^2 
20090928 

From Kathy: My daughter and I are having trouble solving this equation:
x²+ (yz – 3)²
if x=4,y=2 and z=0
We are having difficulty with the x² part of the equation. Thanks Answered by Penny Nom. 





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. 





If 5 to the power of y = 625, what is y? 
20090302 

From Charlene: If 5 to the power of y = 625, what is y? Answered by Penny Nom. 





Comparing 2^3^4^5 ; 2^5^4^3 ; 5^4^3^2 etc. 
20090301 

From JIM: WHICH WOULD BE LARGEST USING THE NUMBERS 2,3,4,5 :
2^3^4^5 ; 2^5^4^3 ; 5^4^3^2 : ETC. OF ALL THE POSSIBLE
COMBINATIONS ? IS THERE A GENERAL FORMULA ? I AM
UNABLE TO FIND A COMPUTER THAT CAN HANDLE SUCH LARGE
CALCULATIONS . I ALSO DO NOT THINK IT IS AS STRAIGHT
FORWARD AS FIRST APPEARS . THANKYOU , JIM Answered by Stephen La Rocque, Robert Dawson and Harley Weston. 





Collecting an army 
20090225 

From bevaz: Question from bevaz, a student:
A ruler orders his chamberlain to collect an army from 30 houses. The servant goes to the first house alone and collects one man. At each house after that he takes the same number of men as he has already collected, so at the second house he goes with one other and so on. How many men did he collect in all? Answered by Penny Nom. 





y = p q^t 
20090212 

From Conor: y= p x (q (to the power t) ) ; y= 100 when t = 2 and y= 4 when t= 0
a) find p and q
b) hence find y when t=4 Answered by Stephen La Rocque. 





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. 





The nth power 
20081212 

From Kellie: I am taking a 9th grade course yet im in 7th grade. I do not understand the nth power
and i have no clue what it is. could you explain to me what it is? Answered by Robert Dawson. 





Equations with fractional powers and roots 
20081112 

From David: Find all real solution to each equation.
x^2/3 = 9 how do you do this if its to the power
x + 1= Square root (3x +13) can you explain how to get an solution with square root? Answered by Penny Nom. 





The nth term of a sequence 
20080913 

From lavett: what is the Nth term in the sequence when the sequence is 2,4,8,16... and the term numbers are 1,2,3,4... Answered by Stephen La Rocque. 





2^x = 1,000,000 
20080906 

From Peter: How do I solve for "x" in the following equation: "2 to the power of x = 1,000,000" ? Answered by Penny Nom. 





The square root of 2 the the X power 
20080905 

From Peter: How can I rewrite the expression: The square root of 2 the the X power? Answered by Penny Nom. 





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. 





Does the sequence 1 2 4 8 16 32 etc have a name? 
20080717 

From Richard: Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name? Answered by Victoria West. 





Arithmetic and powers 
20080430 

From mom: my son and i are trying to do this problem but cant can you help please
4(2)power of 3 3(4) power of 2 i hope you can help thank mom Answered by Penny Nom. 





Why does 2^2 = 4 when 2 * 2 = 4? 
20080422 

From blaine: Why does 2^2 = 4 when 2 * 2 = 4? Answered by Penny Nom. 





Negative Exponents 
20080129 

From Bill: t to the negative fourth power inside parenthesis to the ninth power
OVER
t to the negative fourth power inside parenthesis to the third power
I am confused on how to start the problem. What I did was invert the Ts to make them positive and I then multiplied the powers. I am not sure if this is the correct process. Answered by Harley Weston. 





1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 
20080122 

From Neil: Find the next two terms in the following number sequence
1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128
Find a general rule for the nth term of the sequence Answered by Penny Nom. 





Powers of 2 
20071128 

From Kim: Complete the following:
2 to the power of 4=
2 to the power of 3=
2 to the power of 2=
2 to the power of 1=
If the pattern continues, 2 to the power of 0 = Answered by Penny Nom. 





Two power expressions 
20070929 

From James: find the values for a and b
(a*x to the power of 1*y)(1/2*x*y to the power of b)=6*y to the power of 6
please show me how to do this. Can I begin by taking out the powers? Answered by Leeanne Boehm. 





Is 10 to the power of 1 the same as 10? 
20070917 

From Mac: Is 10 to the power of 1 the same as 10? Answered by Penny Nom. 





X^3 = 3/10 
20070905 

From ioana: If we have X at power 3 that result equally with 3/10 haw much X is ?? Answered by Penny Nom. 





(1+i)^(2i) 
20070426 

From Eilis: How do I solve (1+i) to the power of 2i?
i.e. (1+i)^(2i) Answered by Penny Nom. 





A piece of paper is cut in half 
20070412 

From Jana: A piece of paper is cut in half and one piece is placed on top of the other. Then the two pieces are cut in half and one half is placed on top of the other, forming a stack of four pieces. If this process is carried out a total of 25 times and the original piece of paper is .003 inches thick, what is the height of the stack to the nearest foot.
b. Using the same problem setup: Suppose now that our paper is big enough to fold 50 times. Again the question is “What is the height of the stack of paper,” but this time, “to the nearest mile.” Answered by Stephen La Rocque. 





Large exponents 
20070209 

From Nick: I am trying to figure out an extremely large number. It relates to the estimated number of bacterial divisions in 12775 generations of bacteria. The problem I need to solve is: 2^12775 or 2 to the power of 12,775. Answered by Stephen La Rocque and Penny Nom. 





What is the highest number possible with 3 digits? 
20061116 

From Liz: What is the highest number possible with 3 digits? The teacher said the answer is not 999 and that the question did not say "3digit number." My answer then is 9 to the 99th power (written mathematically of course) as this uses "3 digits" and is obviously a huge number. Is this correct? Answered by Stephen La Rocque. 





The units digit of 12^40 
20061008 

From Lana: FIND THE UNITS DIGIT OF 12 TO THE POWER OF 40. Answered by Penny Nom. 





A base number raised to the power of 0 
20060824 

From Sheila: I'm a 5th grade teacher and need some help with a base number raised to the power of 0 always being 1. My kids asked me why and I told them I'd find out. Answered by Penny Nom. 





A problem with exponents 
20060809 

From A student: (8a to the negative 2 b cube c to the negative 4/4a squared b to the negative 3 c squared) to the negative 2 Answered by Stephen La Rocque. 





2 to the 5th power 
20060619 

From Murray: Is 2 to the 5th power = 32? Answered by Penny Nom. 





I want to calculate 0.00353 to the power 1.3 
20060514 

From Richard: I want to calculate 0.00353 to the power 1.3 How do I do it? Answered by Stephen La Rocque. 





Simplifying with negative exponents 
20060502 

From Kristine:
I am having a hard time understanding factoring and multiplying
polynomials. I have a couple of problems I just can't get, can you
please help me?
Simplify, do not use negatives in the answer:
(5a^{1}b^{7})(2a^{4}b^{2})
and:
(5x^{2}y^{7}z)(4xy^{3}z^{4})
Answered by Stephen La Rocque. 





Degree 
20060209 

From Jessica: I am a 9th grade home school student and have started doing degrees of terms in my math book. The following is some examples they give:
25a to the 4th power is a 4th degree term
67c to the 9th power is a 9th degree term
x is really x to the 1st power so it is a 1st degree term
10 is really 10x to the 0 power so it is a 0 degree term
They go on to say that every constant is a zero degree term.
My question is why isn't a constant, like 10, simply to the 1st power (making is a 1st degree term) like x. Answered by Claude Tardif. 





3^4 and (3)^4 
20051217 

From Brad: What is the answer to
3^{4} = ?
(3)^{4} = ?
(3)^{4} = ? Answered by Penny Nom. 





(2^6) = ? 
20051029 

From Amy: My teacher gave me the problem (2^{6}) on our homework. She marked it wrong when I wrote down 64 for an answer. She said the correct answer was 64. Can you explain why it is 64? Answered by Penny Nom and Leeanne Boehm. 





How do you differentiate y=(x)^(x^x)? 
20050914 

From Calebius: How do you differentiate y=(x)^{(xx)}? Answered by Penny Nom. 





What is the ones digit of 3 to the 79 power? 
20050914 

From Candice: What is the ones digit of 3 to the 79 power? Answered by Penny Nom. 





Manipulating exponents 
20041017 

From A student: I was wondering if you can describe the steps in getting the solution to the problem below. I have the solution of 5/3 in the back of a book, but I have no idea how that answer was reached.
2raised to the 100th power + 2raised to the 98th power divided by 2raised to the 100th power  2raised to the 98th power Answered by Penny Nom. 





Zero to the zero 
20040918 

From Greta: My name is Greta, and I am a 7th grader and my test is coming up. The question I would like to ask you is why 0 elevated to 0 is unidentified. Answered by Penny. 





Algebraic simplification 
20040331 

From Chris: Simplifying Exponents
Question
b^5d^2/b^3d^8 Answered by Penny Nom. 





Evennumbered roots 
20040301 

From A student: I understand that the square root is defined to be positive only. Does
the same rule apply to other evennumbered roots, such as the 4th root, or
the 6th root, etc.? Answered by Harley Weston. 





x^x^x^x^... 
20040123 

From Ryan: you have a number say x and it is to the power of x which is to the power of x and so on infinite times like x^x^x^x^x^x^x^... i have to figure out what x is so that the answer is always 2 Answered by Penny Nom. 





(2^ 20,966,011)  1 
20031212 

From Reid: Can someone please explain, answer and/or solve this: (2^ 20,966,011)  1
I don't know what it means, my boss sent it out, I'm assuming it is to be
solved but don't know what it is, any prompt help would be appreciated, very
much so, in fact, thanks,........... Answered by Penny Nom. 





Notation 
20030915 

From Kim:
Question: i have a couple of questions 1. write in standard form a)4x2x8 b) 5 to the power of 4 . . . Answered by Penny Nom. 





The units digit of 57 to the 28th power 
20030901 

From Maria:
If 57 is raised to the 28th power, what must be the units digit in the result? If you raise 7 to the 500th power, what is the numeral that will appear in the units digit position? Answered by Penny Nom. 





Why is 5 to the 0 power always 1? 
20030824 

From Crystal: Why is 5 to the 0 power always 1? Answered by Penny Nom. 





Solve x = y^z for z 
20030628 

From Nathan: If x = y^z is there a way to solve for z, if x and y are given, without guessing or already knowing the answer?
ie: 64 = 2^z 6 is the obvious value for z. Is there a way I could solve for this variable using a formula, which would also apply when more complex values were substituted for x and y? Answered by Penny Nom. 





5 to the power n 
20030528 

From Sam: What is the integer n for which
5 to the n power + 5 to the n power + 5 to the n power + 5 to the n power + 5 to the n power = 5 to the 25th power? Answered by Penny Nom. 





(x^{y})^{z} = 64 
20030226 

From Melissa: How many ordered triples of positive intergers (xyz) satisfy (x[raised to the y])raised to the z = 64? Answered by Penny Nom. 





The units digit of 2 to the power of 31921 
20021218 

From A student: If 2 to the power of 31921 is multiplied out, what will be the units digit? 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. 





Exponent 0 
20021002 

From Debbi: can you please tell me what the exponent 0 is (i.e. 7^{0}) Answered by Penny Nom. 





Fractional exponents 
20020920 

From Jill: The problem is with fractional exponants: 10 1/3 mult. by 10,000 The 1/3 is an exponant of 10. Answered by Penny Nom. 





The number of decimal places in 1 over a power of 2 
20020912 

From Allan: Does anyone notice that the maximum number of decimal place of the number 2 dividing 1 and its increment (4, 8, 16...etc) is the same as the power of number 2? eg. 2^{2}=4, thus the max number of decimal of ^{1}/_{4}=0.25 which is 2 decimal place and 2 is the number of power of 2 take 64 as example: 2^{6}=64, and take ^{1}/_{64}=0.015625 which has 6 decimal place (and is the power 6) Is there such a law in math? If yes, can you tell me what it is? Or is this my discovery? Answered by Paul Betts. 





8,27,64 . . . 
20020905 

From Mike: We have been trying with no luck all night to complete the following math pattern (next 3 entries) 8,27,64 . . . Any ideas?? Answered by Penny Nom. 





1, 2, 4, 8, 16, 32, etc. 
20020904 

From Ginger: I've been working with finding the nth term for a few weeks, and i can't seem to figure this one out! 1, 2, 4, 8, 16, 32, etc. Answered by Leeanne Boehm. 





(3)to the power 2, divided by 3 
20011031 

From Raz: what is (3)to the power 2, divided by 3= Answered by Penny Nom. 





Zero as an exponent 
20011004 

From Wendy: How do I explain to kids that i.e. 5 exponent 0 = 1? Does 0 exponent 0 = 1? Answered by Leeanne Boehm and 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. 





1996^1999 and 1999^1996 
20010729 

From Rajesh: what is greater 1999^{1997} or 1997^{1999}? Answered by Chris Fisher. 





Powers 
20010304 

From A student: Hey, can you show me how you do .. (2xy)to the 3rd power (x) to the 2nd power? Answered by Penny Nom. 





Exponents 
20010114 

From A student: I am wondering if a number raised to the second power is "squared" and a number raised to the third power is "cubed" is there a name for any number raised to any other power. Answered by Harley Weston. 





Manipulating powers 
20000913 

From Phil: 2^{1/5} x 4^{2/5} = ? Answered by Penny Nom. 





Powers of i 
20000524 

From Paul Fieldhouse: What is the result of raising i to the googol power? is there a rule or pattern to raising i by increasing powers of 10? Answered by Penny Nom. 





The units digit of 3 to the 58th power 
20000510 

From Kylie Mcalpine: the questions we have been asked are what is the units digit of the following: a) 3^{58} b) 23^{58} c) 17^{31} and the harder question of: what is the units digit of the following sum: 13^{841} + 17^{508} + 24^{617} = ??????? Answered by Paul Betts and Penny Nom. 





Factoring ^6 
20000103 

From Athena:
my name is Athena and I have a question on factoring: how would you figure this out: (x^{6}y^{6}) and (x^{6}+y^{6}) Answered by Penny Nom. 





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. 





Powers of zero 
19991031 

From Salina Young: Hello! I have two questions to ask about the power of "0". First, what is the value of "0' to the power of "0"? And why? Second, what is the value of "0" to the power of "2" or '3" etc? And why? Thank you for your help. Answered by Walter Whiteley and Harley Weston. 





(5)^2, 5^2 and (5)^2 
19991013 

From Jennifer Brown: What is the difference between the following problems: (5)^{2}, 5^{2} and (5)^{2} Our text book (Beginning Algebra, fourth edition, published by McGraw Hill, by Streeter, Huthison and Hoetzle) says the second and third problem are exactly the same. I don't see how that can be. Is there a mathematical rule that explains this? Answered by Penny Nom. 





Spreading a rumor 
19990913 

From Bornstar14: There is someone who wants to spread a rumor within 7 days to 250,000,000 people. he wants to know how many people he should tell on the first day (assuming the rumor is passed by everyone who was told to the same amount of people) so that everyone knows on the 7th day. What I did is the 7th root of 250,000,000. this answer is not possible unless rounded. is it okay for the number to be approximate? Answered by Penny Nom. 





A problem with powers 
19990601 

From Bill: solve for the variable: 5^{x} = 25^{x+6} Answered by Penny Nom. 





3 to the power of 1994 
19980905 

From Kim Tangney: What are the last two digits of:  3 to the power of 1994
 7 to the power of 1994
 3 to the power of 1994 + 7 to the power of 1994
 7 to the power of 1994  3 to the power of 1994
Answered by Penny Nom. 





15 to the zero 
19980624 

From Mike Husken: My daughter has the problem: 15 with an exponent of zero=1. Could you help explain why? I would appreciate an answer soon as she has class tomorrow. thanks, Answered by Penny Nom and Patrick Maidorn. 





(50^20)(20^50) 
19980224 

From fion: 50 power of 20 X 20 power of 50? How many zero can be found in the answer and why? Answered by Penny Nom. 





Diagramming Powers 
19971015 

From David Fill: I am a teacher in Massachusettes. We have been diagramming numbers such as two to the third (a 3D cube). One of my students asked me how you would diagram two to the fourth. I have searched through all of my teachers books and cannot seem to find the answer to this question. Is there a way to diagram this? If there is, how would you do this? Your help would be greatly appreciated. Answered by Penny Nom. 





Exponents 
19960225 

From Eric Cote: I want to know why the grade six math books tell you that the little number at the top right of another number (exponent) is called the power, but the grade seven and up books tell you it's called the exponent? Answered by Harley Weston. 





Exposant à la 0 
20000704 

From Sylvie: J'aimerais savoir combien fait 0 exposant 0. Answered by Claude Tardif. 

