Question

Expand:

${\left(4\times 3\right)}^6$

Answer 1

In, ${\left(4\times 3\right)}^6$, $(4\times 3)$ is multiplied $6$ times.

So, ${\left(4\times 3\right)}^6$$=\left(4\times 3\right)\times \left(4\times 3\right)\times \left(4\times 3\right)\times \left(4\times 3\right)\times \left(4\times 3\right)\times \left(4\times 3\right)$

$=(4\times 4\times 4\times 4\times 4\times 4)\times (3\times 3\times 3\times 3\times 3\times 3)$ (Taking the common terms together)

$=4^6\times 3^6$

As, $(4\times 4\times 4\times 4\times 4\times 4)=4^6$ ($4$ is multiplied $6$ times)

Also,$(3\times 3\times 3\times 3\times 3\times 3)=3^6$ ($3$ is multiplied $6$ times)

Therefore, ${\left(4\times 3\right)}^6$$=4^6\times 3^6$.