Question

Simplify and express each of the following in exponential form:${25}^4÷5^3$

Answer 1

Simplying expression: ${25}^4÷5^3$

${\left(25\right)}^4$ can be expressed as $={(5\times 5)}^4$

$={\left(5^2\right)}^4$

${\left(5^2\right)}^4$ can be written as $={\left(5\right)}^{2\times 4}$ …$\mathbf{}\mathbf{[}\mathbf{\because }{\mathbf{\left(}{\mathbf{a}}^{\mathbf{m}}\mathbf{\right)}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{mn}}\mathbf{}\mathbf{]}$

$$\begin{gathered} =5^8 \\ =5^8÷5^3 \\ =5^{8-3}\dots \mathbf{}\mathbf{[}\mathbf{\because }{\mathit{a}}^{\mathbf{m}}\mathbf{}\mathbf{÷}\mathbf{}{\mathit{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathit{a}}^{\mathbf{m}\mathbf{-}\mathbf{n}}\mathbf{]}\mathbf{} \\ =5^5 \end{gathered}$$

Therefore, ${25}^4÷5^3=5^5$