Question

select the equivalent expression.
$left(9^{6} cdot 7^{-9}
ight)^{-4} =?$
choose 1 answer:
a $dfrac{9^{24}}{7^{36}}$
b $9^{24} cdot 7^{-36}$
c $dfrac{7^{36}}{9^{24}}$

Explanation:

Step1: Apply power of a product rule

$$(9^6 \cdot 7^{-9})^{-4} = (9^6)^{-4} \cdot (7^{-9})^{-4}$$

Step2: Apply power of a power rule

$$(9^6)^{-4} = 9^{6 \times (-4)} = 9^{-24}, \quad (7^{-9})^{-4} = 7^{(-9) \times (-4)} = 7^{36}$$

Step3: Rewrite negative exponent as fraction

$$9^{-24} = \frac{1}{9^{24}}$$
$$9^{-24} \cdot 7^{36} = \frac{7^{36}}{9^{24}}$$

Answer:

C. $\frac{7^{36}}{9^{24}}$