Question

Simplify the rational exponent expression as a radical expression.

Answer 1

3√x/y^3

Explanation:

(726x^3y^-18)^1/6

729^1/6*√x*y^-3

3√x/y^3

Answer 2

`\begin{array}{llll} \textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} \end{array} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{( n)/( m)} \implies \sqrt[ m]{a^ n} ~\hspace{10em} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\left(729x^3y^(-18) \right)^{(1)/(6)}\implies \left(3^6x^3y^(-18) \right)^{(1)/(6)}\implies \left(3^{6\cdot (1)/(6)}x^{3\cdot (1)/(6)}y^{-18\cdot (1)/(6)} \right) \\\\\\ 3^1x^{(1)/(2)}y^(-3)\implies 3\sqrt[2]{x^1}\cfrac{1}{y^3}\implies \cfrac{3√(x)}{y^3}`