Question

Write in single exponent form:

${10}^3\times {(-6)}^3$

Answer 1

In ${10}^3\times {(-6)}^3$, there are different bases but the exponents are same.

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

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

${10}^3\times {(-6)}^3$$=(10\times 10\times 10)\times \left[\right(-6)\times (-6)\times (-6\left)\right]$ (Here $a=10,b=-6,m=3$)

$=[10\times (-6\left)\right]\times [10\times (-6\left)\right]\times [10\times (-6\left)\right]$

$={\left(10\times -6\right)}^3$

$={(-60)}^3$

Therefore, ${10}^3\times {(-6)}^3$$={(-60)}^3$.