Question

Evaluate $\frac{{\left(2^2\right)}^3}{2^5}$

Answer 1

Hint: We know one of the law of exponents: ${\left(x^a\right)}^b=x^{a\times b}and\frac{{\left(x\right)}^a}{{\left(y\right)}^b}={\left(x\right)}^{a-b}$

Step 1: Given expression: $\frac{{\left(2^2\right)}^3}{2^5}$

Step2: Solution:

Using the above law of exponents:

$$\begin{gathered} \frac{{\left(2^2\right)}^3}{2^5}=\frac{{\left(2\right)}^{3\times 2}}{{\left(2\right)}^5}\left\{U\sin g{\left(x^a\right)}^b=x^{a\times b}\right\} \\ =\frac{{\left(2\right)}^6}{2^5} \\ ={\left(2\right)}^{6-5}\left\{U\sin g\frac{{\left(x\right)}^a}{{\left(y\right)}^b}={\left(x\right)}^{a-b}\right\} \\ =2 \end{gathered}$$

Hence the answer is $2$