Question

Write the following in exponential form :

$2\times m\times m\times m\times n\times n\times n\times n$

Answer 1

We have the expanded form as :

$2\times m\times m\times m\times n\times n\times n\times n$

Conversion into exponential form :

We have

$2\times m\times m\times m\times n\times n\times n\times n=2\times \left(m\times m\times m\right)\times \left(n\times n\times n\times n\right)$ ( Collecting the same bases in bracket )

$=2\times m^3\times n^4$ ( Using : $a\times a\times a\times a\times a\times ...........ntimes=a^{\mathrm{n}}$ )

$=2m^3{n}^4$

Therefore , $\mathbf{2}\mathbf{}\mathbf{\times }\mathbf{}\mathit{m}\mathbf{}\mathbf{\times }\mathbf{}\mathit{m}\mathbf{}\mathbf{\times }\mathbf{}\mathit{m}\mathbf{}\mathbf{\times }\mathbf{}\mathit{n}\mathbf{}\mathbf{\times }\mathbf{}\mathit{n}\mathbf{}\mathbf{\times }\mathbf{}\mathit{n}\mathbf{}\mathbf{\times }\mathbf{}\mathit{n}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2}{\mathit{m}}^{\mathbf{3}}{\mathit{n}}^{\mathbf{4}}$