If (8^2)p = 8^4, what is the value of p?

Question

Group of answer choices

2

6

3

4

Answer 1

To solve the equation $(8^2)p=8^4$, we can first rewrite the left side:

$$(8^2{)}^p=8^{2p}$$

Now, we equate both sides:

$$8^{2p}=8^4$$

Since the bases are the same, we can set the exponents equal to each other:

$$2p=4$$

Now, divide both sides by 2 to solve for $p$:

$$p=\frac{4}{2}=2$$

The value of $p$ is $\boxed{{\displaystyle 2}}$.