Calculate (9×10×7)^5: Evaluating Products Raised to Powers

We begin by noting that the given expression is $\left(9\times10\times7\right)^5$. Our task is to expand this expression using the power of a product rule.

The power of a product rule states that for any real numbers $a$, $b$, and $c$ and a positive integer $n$, $(a \times b \times c)^n = a^n \times b^n \times c^n$.

Applying this rule to the given expression, we set $a = 9$, $b = 10$, and $c = 7$, and $n = 5$.

By substituting these into the power of a product formula, we have:

• $a^n = 9^5$

• $b^n = 10^5$

• $c^n = 7^5$

Therefore, the expression $\left(9\times10\times7\right)^5$ expands to:

$9^5\times10^5\times7^5$