Question

rewrite the expression using only positive exponents. combine powers with the same base.
$\frac{9^{-3} cdot 5^{-6}}{5^{-10} cdot 9^{4}} = ?$
$\frac{9^{7}}{5^{4}}$
$\frac{5^{4}}{9^{7}}$
$9^{7} cdot 5^{4}$
$\frac{1}{9^{7} cdot 5^{4}}$

Explanation:

Step1: Separate like bases

$\frac{9^{-3}}{9^{4}} \cdot \frac{5^{-6}}{5^{-10}}$

Step2: Apply exponent subtraction rule

For base 9: $9^{-3-4}=9^{-7}$; For base 5: $5^{-6-(-10)}=5^{4}$

Step3: Convert negative exponent

$9^{-7}=\frac{1}{9^{7}}$, so $\frac{1}{9^{7}} \cdot 5^{4} = \frac{5^{4}}{9^{7}}$

Answer:

$\frac{5^{4}}{9^{7}}$ (matches the option $\boldsymbol{\frac{5^4}{9^7}}$)