Question

Write the following in exponential form :

$5\times a\times a\times b\times b\times b\times c\times c\times c\times c$

Answer 1

We have the expanded form as :

$5\times a\times a\times b\times b\times b\times c\times c\times c\times c$

Conversion into exponential form :

We have

$2\times 5\times a\times a\times b\times b\times b\times c\times c\times c\times c=5\times \left(a\times a\right)\times \left(b\times b\times b\right)\times \left(c\times c\times c\times c\right)$ ( Collecting the same bases in bracket )

$=5\times a^2\times b^3\times c^4$ ( Using : $a\times a\times a\times a\times a\times ...........ntimes=a^{\mathrm{n}}$ )

$=5a^2{b}^3{c}^4$

Therefore

$\mathbf{5}\mathbf{}\mathbf{\times }\mathbf{}\mathit{a}\mathbf{}\mathbf{\times }\mathbf{}\mathit{a}\mathbf{}\mathbf{\times }\mathbf{}\mathit{b}\mathbf{}\mathbf{\times }\mathbf{}\mathit{b}\mathbf{}\mathbf{\times }\mathbf{}\mathit{b}\mathbf{}\mathbf{\times }\mathbf{}\mathit{c}\mathbf{}\mathbf{\times }\mathbf{}\mathit{c}\mathbf{}\mathbf{\times }\mathbf{}\mathit{c}\mathbf{}\mathbf{\times }\mathbf{}\mathit{c}\mathbf{}\mathbf{=}\mathbf{}\mathbf{5}{\mathit{a}}^{\mathbf{2}}{\mathit{b}}^{\mathbf{3}}{\mathit{c}}^{\mathbf{4}}$