Question

use positive rational exponents to rewrite the following expression: the square root of x times the 5th root of x

Answer 1

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ \sqrt{x}\cdot \sqrt[5]{x}\implies \sqrt[2]{x^1}\cdot \sqrt[5]{x^1}\implies x^{\frac{1}{2}}\cdot x^{\frac{1}{5}}\impliedby \begin{array}{llll} \textit{same base, thus}\\ \textit{add the exponents} \end{array} \\\\\\ x^{\frac{1}{2}+\frac{1}{5}}\implies x^{\frac{5+2}{10}}\implies x^{\frac{7}{10}}$