Chapter 7.3, Problem 9CYU

To determine

To simplify the given expression.

Answer to Problem 9CYU

  ${343}^{\frac{2}{3}}=49$

Explanation of Solution

Given:

Expression: ${343}^{\frac{2}{3}}$

Formula used:

  $\sqrt[b]{a^c}=a^{\frac{c}{b}}$

Calculation:

Consider the given expression,

  ${343}^{\frac{2}{3}}$

Here, 343 can be written as $7^3.$

Substituting the above formula in the given expression,

  $\begin{array}{l}$ \Rightarrow {(7^3)}^{\frac{2}{3}}$\Rightarrow 7^{\frac{3\times 2}{3}}\\ \Rightarrow 7^2\\ \Rightarrow 49\end{array}$

Conclusion:

Therefore, the simplified form of the equation is 49.