Question

Simplify and write $\left(6^2\times 6^4\right)÷6^3$ as a single exponent.

Answer 1

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

$$\begin{gathered} a^m\times a^n=a^{m+n} \\ \frac{a^m}{a^n}=a^{m-n} \end{gathered}$$

On solving step by step now, we get :

Firstly, $\left(6^2\times 6^4\right)=6^{2+4}=6^6$

Then, $6^6÷6^3=6^{6-3}=6^3$

So, we have $\left(6^2\times 6^4\right)÷6^3$$=\left(6^{2+4}\right)÷6^3=6^6÷6^3=6^{6-3}=6^3$

Hence, $\left(6^2\times 6^4\right)÷6^3$ is equal to $6^3$.