Question

Write the single radical expression for : ^4√x*^5√2x

Answer 1

\[\large \sqrt[4]{x^5}\sqrt[5]{2x}\]


\[\large (x^5)^{\frac{1}{4}}(2x)^{\frac{1}{5}}\]


\[\large (x^5)^{\frac{5}{20}}(2x)^{\frac{4}{20}}\]


\[\large \left((x^5)^5(2x)^4\right)^{\frac{1}{20}}\]


\[\large \sqrt[20]{(x^5)^5(2x)^4}\]


\[\large \sqrt[20]{x^{25}(16x^4)}\]


\[\large \sqrt[20]{16x^{29}}\]
So \[\large \sqrt[4]{x^5}\sqrt[5]{2x}=\sqrt[20]{16x^{29}}\]