Question

Simplify ${(-2)}^{200}÷2^{50}$& write in exponential form.

Answer 1

Given expression : ${(-2)}^{200}÷2^{50}$

$$\begin{gathered} ={\left[\left(-1\right)\times 2\right]}^{200}÷2^{50} \\ =[{(-1)}^{200}\times 2^{200}]÷2^{50} \\ =\left[1\times 2^{200}\right]÷2^{50}\left\{\sin ce,{(-1)}^{Evennumber}=1\right\} \\ =2^{200}÷2^{50} \\ =2^{200-50}(\sin ce,a^m÷a^n=a^{m-n}) \\ =2^{150} \end{gathered}$$

Hence, ${(-2)}^{200}÷2^{50}$can be written as $2^{150}$in exponential form.