Question

Represent ${(-7)}^3\times a^3\times b^3$ as a single exponent.

Answer 1

We know that for any non-zero integers $\text{'}a\text{'}$, $\text{'}b\text{'}$ and $\text{'}c\text{'}$ and for any natural number $\text{'}n\text{'}$, we have, $a^n\times b^n\times c^n={\left(a\times b\times c\right)}^n$.

So, on applying, we get:${(-7)}^3\times a^3\times b^3$$={(-7\times a\times b)}^3={(-7ab)}^3$

Hence, ${(-7)}^3\times a^3\times b^3$ as a single exponent is equal to ${(-7ab)}^3$.