Question

which expression is equivalent to ((2 cdot 9)^4)? (2 cdot 9^4) (2^4 cdot 9) (2^9 cdot 4^9) (2^4 cdot 9^4)

Explanation:

Step1: Recall exponent product rule

For any real numbers $a, b$ and positive integer $n$, $(a \cdot b)^n = a^n \cdot b^n$.

Step2: Apply rule to given expression

Substitute $a=2$, $b=9$, $n=4$:
$$(2 \cdot 9)^4 = 2^4 \cdot 9^4$$

Answer:

$2^4 \cdot 9^4$