Chapter 7.3, Problem 11CYU

To determine

To simplify the given expression.

Answer to Problem 11CYU

1296

Explanation of Solution

Given:

Expression: ${216}^{\frac{4}{3}}$

Formula used:

  $x^{\frac{a}{b}}=\sqrt[b]{x^a}$

Calculation:

Consider the given expression ${216}^{\frac{4}{3}}$ ,

Applying the above formula,

  ${216}^{\frac{4}{3}}=\sqrt[3]{{\left(216\right)}^4}$

Here, 216 can be written as $6^3.$

  $\begin{array}{c}{216}^{\frac{4}{3}}=\sqrt[3]{{\left(216\right)}^4}\\ =\sqrt[3]{{\left(6^3\right)}^4}\\ =6^{\frac{3\times 4}{3}}\\ =6^4\\ =1296\end{array}$

Conclusion:

Therefore, the simplified form of the expression is 1296.