Question

Compute and write the result in exponential form :

${\left(2^8\right)}^4\times \frac{1}{{\left(2^6\right)}^3}$

Answer 1

Find the required exponential form

Given ${\left(2^8\right)}^4\times \frac{1}{{\left(2^6\right)}^3}$

$\Rightarrow {\left(2\right)}^{8\times 4}\times \frac{1}{{\left(2\right)}^{6\times 3}}$ [ by using the ${\left(a^m\right)}^n=a^{m\times n}$ ]

$$\begin{gathered} \Rightarrow {\left(2\right)}^{32}\times \frac{1}{{\left(2\right)}^{18}} \\ \Rightarrow {\left(2\right)}^{32-18}\left[:.byu\sin g{a}^m÷a^n=a^{m-n}\right] \end{gathered}$$

$\Rightarrow {\left(2\right)}^{14}$

Hence, the exponential form of ${\left(2^8\right)}^4\times \frac{1}{{\left(2^6\right)}^3}$is ${\left(2\right)}^{14}.$