Question

Simplify and write in the exponential notation: ${\left[{\left(-6\right)}^2\right]}^4÷{(-6)}^6$

Answer 1

Simplifying the exponent :

Given exponential is: ${\left[{\left(-6\right)}^2\right]}^4÷{(-6)}^6$

Some of the laws of exponential are:

1. ${\left(x^a\right)}^b=x^{a\times b}$
2. $x^a÷x^b=x^{a-b}$
3. ${(-x)}^n={\left(x\right)}^{n}ifniseven$

$=-{\left(x\right)}^{n}ifnisodd$

Using the above law of exponential:

$$\begin{gathered} {\left[{\left(-6\right)}^2\right]}^4÷{(-6)}^6={(-6)}^{4\times 2}÷{(-6)}^6 \\ ={(-6)}^8÷{(-6)}^6 \\ ={(-6)}^{8-6}\{U\sin g{x}^a÷x^b=x^{a-b}\} \\ ={(-6)}^2\{As2iseven\} \end{gathered}$$

Hence, ${\left[{\left(-6\right)}^2\right]}^4÷{(-6)}^6=$${(-6)}^2$