
Name: Carissa
Who is asking: Student
Level: Middle
Question:
how do you work this out? Investigate the relationship between a,b,c and d if 2^{a}*2^{b}=4^{c}/4^{d}?
Hi Carissa,
Hi Carissa,
To find the relationship between a, b, c and d, you must first know the rules of exponents:
 When you multiply two numbers with the same base, you add the exponents
eg. a^{2} * a^{3} = a^{2+3} = a^{5}
 When you divide two numbers with the same base, you subtract the exponentÊof the number in the denominator from the exponent of the number in the numerator.
eg. a^{5}/a^{2} = a^{52} = a^{3}
 When you raise a power to another power, you multiply the exponents
eg. (a^{3})^{2} = a^{2*3} = a^{6}
You will need to apply all three of these rules to find the relationship between a, b, c and d in your problem:
2^{a} * 2^{b} = 4^{c}/4^{d}   This is given. First apply rule 1 to lefthand side 
2^{a+b} = 4^{c}/4^{d}   Now apply rule 2 to righthand side 
2^{a+b} = 4^{cd}   We need to have the same base on both sides, so rewrite 4 as 2^{2} 
2^{a+b} = (2^{2})^{cd}   Now apply rule 3 to the righthand side 
2^{a+b} = 2^{2(cd)}   Since we have the same base on both sides (i.e. 2), and the righthand side equals the lefthand side, we know that the exponents must be equal 
Therefore, a + b = 2(c  d) This is the relationship between a, b,Êc and d
Cheers,
Leeanne
Go to Math Central

