Question

Write the following in exponential form :

$3\times 7\times b\times b\times c\times c\times c\times c$

Answer 1

We have the expanded form as :

$3\times 7\times b\times b\times c\times c\times c\times c$

Conversion into exponential form :

We have

$3\times 7\times b\times b\times c\times c\times c\times c=3\times 7\times \left(b\times b\right)\times \left(c\times c\times c\times c\right)$ ( Collecting the same bases in bracket )

$=21\times b^2\times c^4$ ( Using : $a\times a\times a\times a\times a\times ...........ntimes=a^{\mathrm{n}}$ )

$=21b^2{c}^4$

Therefore

$\mathbf{3}\mathbf{}\mathbf{\times }\mathbf{7}\mathbf{}\mathbf{\times }\mathit{b}\mathbf{}\mathbf{\times }\mathbf{}\mathit{b}\mathbf{}\mathbf{\times }\mathbf{}\mathit{c}\mathbf{}\mathbf{\times }\mathbf{}\mathit{c}\mathbf{}\mathbf{\times }\mathbf{}\mathit{c}\mathbf{}\mathbf{\times }\mathbf{}\mathit{c}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{21}{\mathit{b}}^{\mathbf{2}}{\mathit{c}}^{\mathbf{4}}$