Question

Fill in the blanks :

${\left({\left(-1000\right)}^0\right)}^2÷2^3=\_\_\_\_\_\_\_\_$

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 -

$$\begin{gathered} {\left({\left(-1000\right)}^0\right)}^2÷2^3={\left(-1000\right)}^{0\times 2}÷2^3 \\ ={\left(-1000\right)}^0÷8 \\ =1÷8 \\ =\frac{1}{8} \end{gathered}$$

Hence, the correct answer is $\frac{1}{8}$.