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?

(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