Chapter 7, Problem 21MCQ

To determine

To Simplify: The expression $8^{\frac{2}{3}}$

Answer to Problem 21MCQ

  $8^{\frac{2}{3}}=4$

Explanation of Solution

Given information:

The expression $8^{\frac{2}{3}}$

Concept and Formula Used:

Rule of exponent.

  $\sqrt[n]{a}=a^{\frac{1}{n}},{\left(ab\right)}^n=a^n{b}^n$

BODMAS rule

Calculation:

The given expression is

  $\begin{array}{l}{8}^{\frac{2}{3}}={\left(2\times 2\times 2\right)}^{\frac{2}{3}}\\ 8^{\frac{2}{3}}={\left(2^3\right)}^{\frac{2}{3}}\\ \text{Using }{\left(a^m\right)}^n=a^{m\times n}\\ 8^{\frac{2}{3}}={\left(2\right)}^{3\times \frac{2}{3}}\\ 8^{\frac{2}{3}}={\left(2\right)}^2\\ 8^{\frac{2}{3}}=4\end{array}$

Conclusion:

  $8^{\frac{2}{3}}=4$