Question

Fill in the blanks :

${\left({\left(-100\right)}^2\right)}^0÷2^2=\_\_\_\_\_\_\_\_$

Answer 1

Compute the required value:

By the properties of exponent, we know that -

$$\begin{gathered} {\left(a^x\right)}^y=a^{x\times y} \\ {a}^0=1 \end{gathered}$$

By using the above properties -

$$\begin{gathered} {\left({\left(-100\right)}^2\right)}^0÷2^2={\left(-100\right)}^{2\times 0}÷2^2 \\ ={\left(-100\right)}^0÷4 \\ =1÷4 \\ =\frac{1}{4} \end{gathered}$$

Hence, the correct answer is $\frac{1}{4}$.