Question

Evaluate the value of the following:

${\left[{\left(-4\right)}^0\right]}^8-{(-1)}^{21}$

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. $$\begin{gathered} {(-1)}^n=1ifniseven \\ =-1ifnisodd \end{gathered}$$
3. ${\left(x\right)}^0=1$

Step 1: Given number: ${\left[{\left(-4\right)}^0\right]}^8-{(-1)}^{21}$

Step2: Solution:

Using the above law of exponents:

$$\begin{gathered} {\left[{\left(-4\right)}^0\right]}^8-{(-1)}^{21}={(-4)}^{0\times 8}-{\left(-1\right)}^{21};\{U\sin g{\left(x^a\right)}^b=x^{a\times b}\} \\ ={(-4)}^0-(-1);\{As21isodd\} \\ =1+1=2;\{U\sin g{\left(x\right)}^0=1\} \end{gathered}$$

$2$, This is the required value.

Therefore $2$, This is the required value.