Question

Write the following in product form :

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

Answer 1

Given the algebraic expression in exponential form as : $3a^2{b}^3{c}^4$

Conversion of algebraic expression from exponential form to product form :

Knowing that :

${\mathit{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}\mathit{a}\mathbf{}\mathbf{\times }\mathit{a}\mathbf{}\mathbf{\times }\mathit{a}\mathbf{}\mathbf{\times }\mathit{a}\mathbf{}\mathbf{\times }\mathbf{}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{}\mathit{n}\mathbf{}\mathit{t}\mathit{i}\mathit{m}\mathit{e}\mathit{s}$

we get

$$\begin{gathered} 3a^2{b}^3{c}^4=3\times a^2\times b^3\times c^4 \\ =3\times a\times a\times b\times b\times b\times c\times c\times c\times c \end{gathered}$$

Therefore product form of the give expression is :

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