Question

Evaluate the value of the following:

$\frac{2^2\times {(-1)}^6}{{(-2)}^4}$

Answer 1

Finding the value of exponential expression

Given expression is $\frac{2^2\times {(-1)}^6}{{(-2)}^4}$

We know that,

1. $\frac{x^a}{x^b}=x^{a-b}$
2. $$\begin{gathered} {(-x)}^n={\left(x\right)}^{n}ifniseven \\ =-{\left(x\right)}^{n}ifnisodd \end{gathered}$$
3. ${\left(x\right)}^{-n}=\frac{1}{\left(x\right)}$

Therefore,

$\begin{array}{rcl}\frac{2^2\times {(-1)}^6}{{(-2)}^4}& =& \frac{2^2\times {\left(1\right)}^6}{{\left(2\right)}^4}\{As4and6areeven\}\\ & =& 2^{2-4}\left\{U\sin g\frac{x^a}{x^b}=x^{a-b}\right\}\\ & =& 2^{-2}\\ & =& \frac{1}{2^2}\left\{U\sin g{\left(x\right)}^{-n}=\frac{1}{{\left(x\right)}^n}\right\}\\ & =& \frac{1}{4}\end{array}$

Hence, $\frac{2^2\times {(-1)}^6}{{(-2)}^4}=\frac{1}{4}$