Question

Simplify :$\left({\left(2^5\right)}^2\times 7^3\right)/\left(8^3\times 7\right)$

Answer 1

Given $\left({\left(2^5\right)}^2\times 7^3\right)/\left(8^3\times 7\right)$

$\begin{array}{c}\left({\left(2^5\right)}^2\times 7^3\right)/\left(8^3\times 7\right)=\frac{\left({\left(2^5\right)}^2\times 7^3\right)}{8^3\times 7}\\ =\frac{\left({\left(2^5\right)}^2\times 7^3\right)}{{\left(2^3\right)}^3\times 7}\\ =\frac{2^{10}\times 7^3}{2^9\times 7}\\ =2^{10-9}\times 7^{3-1}\mathbf{[}\mathbf{\because }{\mathit{a}}^{\mathbf{m}\mathbf{}}\mathbf{÷}{\mathit{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}{\mathit{a}}^{\mathbf{m}\mathbf{-}\mathbf{n}}\mathbf{]}\\ =2\times 7^2\\ =2\times 49\\ =98\end{array}$

Hence, the simplified form of $\left({\left(2^5\right)}^2\times 7^3\right)/\left(8^3\times 7\right)$ is $98$.