Question

$$\sqrt[ 3 ]{ 8 { x }^{ { 6 }^{ } } { y }^{ 3 } }$$

Answer

$$2*x^(6^/3)*y$$

Solution


Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\sqrt[3]{8}\sqrt[3]{{x}^{{6}^{}}}\sqrt[3]{{y}^{3}}\]
Calculate.
\[2\sqrt[3]{{x}^{{6}^{}}}\sqrt[3]{{y}^{3}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[2{x}^{{6}^{}\times \frac{1}{3}}\sqrt[3]{{y}^{3}}\]
Simplify  \({6}^{}\times \frac{1}{3}\)  to  \(\frac{{6}^{}}{3}\).
\[2{x}^{\frac{{6}^{}}{3}}\sqrt[3]{{y}^{3}}\]
Use this rule: \(\sqrt[3]{{x}^{3}}=x\).
\[2{x}^{\frac{{6}^{}}{3}}y\]