Question

Simplify and write ${\left(3^3\right)}^5\times {\left(3^4\right)}^2$as a single exponent.

Answer 1

As we already know for any non-zero integer $\text{'}a\text{'}$ and natural numbers $m$ and $n$,

$$\begin{gathered} {\left(a^m\right)}^n=a^{m\times n}=a^{mn} \\ {a}^m\times a^n=a^{m+n} \end{gathered}$$

On solving now, we get :

${\left(3^3\right)}^5\times {\left(3^4\right)}^2$$=3^{3\times 5}\times 3^{4\times 2}=3^{15}\times 3^8=3^{15+8}=3^{23}$

Hence, ${\left(3^3\right)}^5\times {\left(3^4\right)}^2$ is equal to $3^{23}$.