Question

Write in single exponent form:

$a^3\times {(-b)}^3$

Answer 1

In $a^3\times {(-b)}^3$, there are different bases but the exponents are same.

So, for any non-zero integers $a,b$ where $m$ is any whole number,

$a^m\times b^m={\left(ab\right)}^m$

$a^3\times {(-b)}^3$$=(a\times a\times a)\times \left[\right(-b)\times (-b)\times (-b\left)\right]$ (Here $a=a,b=-b,m=3$)

$=[a\times (-b\left)\right]\times [a\times (-b\left)\right]\times [a\times (-b\left)\right]$

$={\left(a\times -b\right)}^3$

$={(-ab)}^3$

Therefore, $a^3\times {(-b)}^3$$={(-ab)}^3$.