Question

which expression is equivalent to \\((2^7 \cdot 3^{-5} \cdot 9)^4\\)?

\\(\bigcirc\\) \\(2^7 \cdot 3^{-5} \cdot 9^4\\)
\\(\bigcirc\\) \\(2^{28} \cdot (-3)^{20} \cdot 9^4\\)
\\(\bigcirc\\) \\(2^{28} \cdot 3^{-20} \cdot 9^4\\)
\\(\bigcirc\\) \\(2^{11} \cdot 3^{-1} \cdot 9^5\\)

Explanation:

Step1: Apply the power of a product rule

$$(2^{7} \cdot 3^{-5} \cdot 9)^{4} = (2^{7})^{4} \cdot (3^{-5})^{4} \cdot 9^{4}$$

Step2: Simplify the exponents

$$2^{7 \cdot 4} \cdot 3^{-5 \cdot 4} \cdot 9^{4} = 2^{28} \cdot 3^{-20} \cdot 9^{4}$$

Answer:

\(2^{28} \cdot 3^{-20} \cdot 9^{4}\)