Question

Question 38

In the following question, fill in the blanks to make the statements true.

The value of ${\left(\frac{1}{2^3}\right)}^2$is equal to ___

Answer 1

Using the law of exponents ,
$(a^m{)}^n=(a{)}^{mn}$

$\therefore {\left(\frac{1}{2^3}\right)}^2={\left(\frac{1^3}{2^3}\right)}^2={\left(\frac{1}{2}\right)}^{3\times 2}$

$={\left(\frac{1}{2}\right)}^6=\frac{1}{2^6}=\frac{1}{64}$