Chapter 6.6, Problem 43PPS

To determine

The simplified form of the expression ${64}^{\frac{1}{3}}-{32}^{\frac{1}{3}}+8^{\frac{1}{3}}$ .

Answer to Problem 43PPS

The simplified form of expression ${64}^{\frac{1}{3}}-{32}^{\frac{1}{3}}+8^{\frac{1}{3}}$ is $6-2^{\frac{5}{3}}$ .

Explanation of Solution

Given information: The given expression is ${64}^{\frac{1}{3}}-{32}^{\frac{1}{3}}+8^{\frac{1}{3}}$ .

Calculation: The given expression ${64}^{\frac{1}{3}}-{32}^{\frac{1}{3}}+8^{\frac{1}{3}}$ can be simplified as,

  $\begin{array}{c}{64}^{\frac{1}{3}}-{32}^{\frac{1}{3}}+8^{\frac{1}{3}}={\left(2^6\right)}^{\frac{1}{3}}-{\left(2^5\right)}^{\frac{1}{3}}+{\left(2^3\right)}^{\frac{1}{3}}\mathrm{......}\left(\text{Factorized}\right)\\ ={\left(2\right)}^2-{\left(2\right)}^{\frac{5}{3}}+{\left(2\right)}^1\mathrm{......}\left(\text{Simplified}\right)\\ =4-{\left(2\right)}^{\frac{5}{3}}+2\\ =6-2^{\frac{5}{3}}\end{array}$