Question

(✗ An equation is shown.

(3 ^ - 2) / (3 ^ p) = 3 ^ 4

What is the value of p?

A

6

B 2

X

C

-2

D

-6

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can simplify the left side first by applying the rules of exponents.

(3 ^ -2) / (3 ^ p) = 3 ^ 4

(1 / 3^2) / 3^p = 3^4

1/9 * 1/3^p = 3^4

1/9 * 1/3^p = 3 ^ 4

1/9 * 3 ^ -p = 3 ^ 4

3 ^ -2 - p = 3 ^ 4

Now we can equate the exponents on both sides:

-2 - p = 4

Solving for p:

-p = 6

p = -6

Therefore, the value of p is -6.

The answer is D) -6.