Question

rewrite the expression using only positive exponents. combine powers with the same base.$\frac{(9^{-3} cdot 2^{-7})^{2}}{9^{5}} =?LXB0\frac{2^{14}}{9^{11}}LXB1\frac{1}{9^{11} cdot 2^{14}}$

Explanation:

Step1: Apply power of a product rule

$$\frac{(9^{-3})^2 \cdot (2^{-7})^2}{9^5}$$

Step2: Apply power of a power rule

$$\frac{9^{-6} \cdot 2^{-14}}{9^5}$$

Step3: Subtract exponents for same base

$$9^{-6-5} \cdot 2^{-14} = 9^{-11} \cdot 2^{-14}$$

Step4: Convert to positive exponents

$$\frac{1}{9^{11} \cdot 2^{14}}$$

Answer:

$\frac{1}{9^{11} \cdot 2^{14}}$