Question

what is the value of $9^{-y}$ if $9^y = 729$? (a) -729 (b) $\frac{1}{729}$ (c) $\frac{1}{9}$ (d) 81 (e) 729

Explanation:

Step1: Recall negative exponent rule

For any non-zero base $a$ and exponent $n$, $a^{-n} = \frac{1}{a^n}$. So $9^{-y} = \frac{1}{9^y}$.

Step2: Substitute given value

We know $9^y = 729$, so substitute into the expression:
$\frac{1}{9^y} = \frac{1}{729}$

Answer:

(B) $\frac{1}{729}$