Question

which expression is equivalent to \\((9 \cdot 8)^4\\)?

\\(\bigcirc (9^4)^8\\)

\\(\bigcirc 9 \cdot 8 \cdot 4\\)

\\(\bigcirc 9^4 \cdot 8^4\\)

\\(\bigcirc (9^8)^4\\)

Explanation:

Step1: Identify the exponent rule

Apply the power of a product rule:

$$(a \cdot b)^{n} = a^{n} \cdot b^{n}$$

Step2: Simplify the expression

Substitute \(a = 9\), \(b = 8\), and \(n = 4\):

$$(9 \cdot 8)^{4} = 9^{4} \cdot 8^{4}$$

Answer:

\(9^{4} \cdot 8^{4}\)