Question

Correct answer will get marked. (Worth 50 Points)

If (7^2)p = 7^6, what is the value of p?

2
3
4
8

Answer 1

p = 3 (choice B)

Explanation:

(7^2)^p = 7^6

7^(2p) = 7^6

The bases are equal to 7, so the exponents must be equal for the two sides to be the same, meaning that

2p = 6

2p/2 = 6/2

p = 3

Sure enough we see that

(7^2)^p = 49^p = 49^3 = 117649

7^6 = 117649

which confirms that (7^2)^p = 7^6 is a true equation when p = 3