What is (x^{-1})/(3y^{-1)} ?

The solution to (x^{-1})/(3y^{-1)} is y/(3x)

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simplify (x^{-1})/(3y^{-1)}

simplify

\frac{x ^{- 1}}{3 y ^{- 1}}

\frac{y}{3 x}

Solution steps

\frac{x ^{- 1}}{3 y ^{- 1}}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

x^{- 1} = \frac{1}{x}

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

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{1}{x \cdot 3 y ^{- 1}}

Simplify

x \cdot 3 y^{- 1} : \frac{3 x}{y}

= \frac{1}{\frac{3 x}{y}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{y}{3 x}

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