Question

Simplify and express the result in power of $3$ :

$\left(4^2\times 4^3\right)÷4^5$.

Answer 1

Given; $\left(4^2\times 4^3\right)÷4^5$.

We know that

${\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}+\mathrm{n}}$

${\mathrm{a}}^{\mathrm{m}}÷{\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}$

Now,

$\left(4^2\times 4^3\right)÷4^5=\left(4^{2+3}\right)÷4^5\left[\because {\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}+\mathrm{n}}\right]$

$$\begin{gathered} =4^5÷4^5 \\ =4^{5-5}\left[\because {\mathrm{a}}^{\mathrm{m}}÷{\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}\right] \\ =4^0 \\ =1 \\ =1^3 \end{gathered}$$

Hence, $\left(4^2\times 4^3\right)÷4^5=1$ or $1^3$.