Question

write the expression as the product of two powers.
$(13\cdot 14)^3 = \\ 13^3\cdot 14^3$
how can you write any expression of the form $(a\cdot b)^m$ as the product of two powers?
$(a\cdot b)^m =$?
$a\cdot b^m$
$a\cdot b^{m - 1}$
$a^m\cdot b$
$a^m\cdot b^m$

Explanation:

Step1: Recall exponent product rule

The power of a product rule states that when raising a product of two terms to an exponent, we distribute the exponent to each term in the product.

Step2: Apply rule to $(a \cdot b)^m$

By the power of a product rule, $(a \cdot b)^m = a^m \cdot b^m$, which matches the given example $(13 \cdot 14)^3 = 13^3 \cdot 14^3$.

Answer:

$a^m \cdot b^m$