Question

Evaluate the value of the following:

${\left[{\left(-8\right)}^2\right]}^2$

Answer 1

Hint: As we know the following laws of exponents is:

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

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

Step 1: Given number: ${\left[{\left(-8\right)}^2\right]}^2$

Step2: Solution:

Using the above law of exponents:

$$\begin{gathered} {\left[{\left(-8\right)}^2\right]}^2={(-8)}^{2\times 2}\{U\sin g{\left(x^a\right)}^b=x^{a\times b}\} \\ ={(-8)}^4 \\ =4096\{As4iseven\} \end{gathered}$$

Hence, $4096$, is the required value.