Question

the expression (4^p*4^1)^3 simplifies to 4^15. Eric was asked to find the value of p and said the answer is p=11. Is Eric correct? why or why not. If not what does p equal?

Answer 1

(4^p*4^1)^3  = 4^15

add the exponents

(4^(p+1))^3 = 4^15

power to the power means multiply

(4^3(p+1)) = 4^15

the bases are the same so the powers have to be the same

3(p+1)) = 15

divide by 3

p+1 =5

subtract 1

p=4

Eric is incorrect.  p=4