Question

Express in exponential form:
$\sqrt[3]{3{xy}^2}÷x^{2}y$

Answer 1

$={\left(x{y}^2\right)}^{\frac{1}{3}}÷x^{2}y$

$=\frac{x^{\frac{1}{3}}{y}^{\frac{2}{3}}}{x^{2}y}$ [$(a^m{)}^n=a^{mn}$]

$=x^{\frac{1}{3}-2}{y}^{\frac{2}{3}-1}$ [$a^m÷a^n=a^{m-n}$]

$=x^{\frac{1-6}{3}}{y}^{\frac{2-3}{3}}$

$=x^{\frac{-5}{3}}{y}^{\frac{-1}{3}}$

$=(\frac{1}{x^{5}y}{)}^{\frac{1}{3}}$ [$a^{-1}=\frac{1}{a},a\ne =0$]