Question

select all the expressions that are equivalent to $9^{-5} \cdot 9$.
$\frac{1}{9^{-4}}$
$9^{-5}$
$9^{-4}$
$\frac{1}{9^{-5}}$

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $9^{-5} \cdot 9^1 = 9^{-5+1}$

Step2: Calculate the exponent

$9^{-5+1} = 9^{-4}$

Step3: Rewrite using negative exponent rule

A negative exponent means reciprocal: $9^{-4} = \frac{1}{9^{4}}$, and $\frac{1}{9^{-4}} = 9^{4}$ (not equivalent), $9^{-5}$ is the original first term (not equivalent), $\frac{1}{9^{-5}} = 9^{5}$ (not equivalent)

Answer:

$9^{-4}$