Question

which expression is equivalent to $5^2 \cdot 7^2$?\
$(5 \cdot 2)^7$ $(5 \cdot 7)^2$ $(5 \cdot 2)^2$ $(2 \cdot 7)^5$

Explanation:

Step1: Recall exponent product rule

For non-zero numbers $a$ and $b$, $a^n \cdot b^n = (a \cdot b)^n$

Step2: Match to given expression

Here $a=5$, $b=7$, $n=2$, so $5^2 \cdot 7^2 = (5 \cdot 7)^2$

Answer:

$(5 \cdot 7)^2$