Which two expressions are equivalent to each other?

To determine which two expressions are equivalent, we can simplify each expression using the laws of exponents.

1. 9^-5 remains as it is.
2. (9^2)^-3 can be simplified to 9^(2 * -3) = 9^-6.
3. 9^9 / 9^4 simplifies to 9^(9 – 4) = 9^5.
4. 9^4 · 9^-9 simplifies to 9^(4 + (-9)) = 9^(-5).

Now, let’s compare the simplified forms:

– 9^-5

– 9^-6

– 9^5

– 9^-5

The two equivalent expressions are 9^-5 and 9^4 · 9^-9 (both simplify to 9^-5).

So, the answer is that 9^-5 and 9^4 · 9^-9 are equivalent to each other.