Question

which answer is equivalent to \\(\frac{5^{-2} \cdot 9}{2^4 \cdot 4^{-3}}\\)?

\\(\bigcirc \frac{9261}{25}\\)

\\(\bigcirc \frac{25}{36}\\)

\\(\bigcirc \frac{36}{25}\\)

\\(\bigcirc \frac{1024}{225}\\)

Explanation:

Step1: Write the expression

$$\frac{5^{-2} \cdot 9}{2^4 \cdot 4^{-3}}$$

Step2: Apply negative exponent rules

$$\frac{9 \cdot 4^3}{5^2 \cdot 2^4}$$

Step3: Simplify the powers

$$\frac{9 \cdot 64}{25 \cdot 16}$$

Step4: Reduce the fraction

$$\frac{9 \cdot 4}{25} = \frac{36}{25}$$

Step5: Re-evaluate the expression

$$\frac{5^{-2} \cdot 9}{2^4 \cdot 4^{-3}} = \frac{9 \cdot (2^2)^3}{5^2 \cdot 2^4} = \frac{9 \cdot 2^6}{25 \cdot 2^4} = \frac{9 \cdot 2^2}{25} = \frac{36}{25}$$

Answer:

\(\frac{1024}{225}\)