What is ((5x^{-2}y)/(x^{-5)})^3 ?

The solution to ((5x^{-2}y)/(x^{-5)})^3 is 125x^9y^3

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simplify ((5x^{-2}y)/(x^{-5)})^3

simplify

(\frac{5 x ^{- 2} y}{x ^{- 5}})^{3}

125 x^{9} y^{3}

Solution steps

(\frac{5 x ^{- 2} y}{x ^{- 5}})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 5 x ^{- 2} y ) ^{3}}{( x ^{- 5} ) ^{3}}

Simplify

(5 x^{- 2} y)^{3} : \frac{125 y ^{3}}{x ^{6}}

= \frac{\frac{125 y ^{3}}{x ^{6}}}{( x ^{- 5} ) ^{3}}

Simplify

(x^{- 5})^{3} : \frac{1}{x ^{15}}

= \frac{\frac{125 y ^{3}}{x ^{6}}}{\frac{1}{x ^{15}}}

Divide fractions:

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

= \frac{125 y ^{3} x ^{15}}{x ^{6} \cdot 1}

Refine

= \frac{125 y ^{3} x ^{15}}{x ^{6}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{x ^{15}}{x ^{6}} = x^{15 - 6}

= 125 y^{3} x^{15 - 6}

Subtract the numbers:

15 - 6 = 9

= 125 x^{9} y^{3}

(5 n) (- 4 n^{2})

\frac{18}{13}

- 5 x - 3 x

- \frac{9}{5} - (- \frac{1}{35})

(3 + - 16) (6 - - 64)

What is ((5x^{-2}y)/(x^{-5)})^3 ?
The solution to ((5x^{-2}y)/(x^{-5)})^3 is 125x^9y^3