What is (8xy)^{-2}*(x^{-5}y^{-1})/(xy) ?

The solution to (8xy)^{-2}*(x^{-5}y^{-1})/(xy) is 1/(64x^8y^4)

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simplify (8xy)^{-2}*(x^{-5}y^{-1})/(xy)

simplify

(8 x y)^{- 2} \cdot \frac{x ^{- 5} y ^{- 1}}{x y}

\frac{1}{64 x ^{8} y ^{4}}

Solution steps

(8 x y)^{- 2} \frac{x ^{- 5} y ^{- 1}}{x y}

Simplify

(8 x y)^{- 2} : \frac{1}{64 x ^{2} y ^{2}}

= \frac{1}{64 x ^{2} y ^{2}} \cdot \frac{x ^{- 5} y ^{- 1}}{x y}

Cancel

\frac{x ^{- 5} y ^{- 1}}{x y} : \frac{1}{x ^{6} y ^{2}}

= \frac{1}{64 x ^{2} y ^{2}} \cdot \frac{1}{x ^{6} y ^{2}}

Apply the fraction rule:

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

= \frac{1 \cdot 1}{64 x ^{2} y ^{2} x ^{6} y ^{2}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{64 x ^{2} y ^{2} x ^{6} y ^{2}}

Simplify

64 x^{2} y^{2} x^{6} y^{2} : 64 x^{8} y^{4}

= \frac{1}{64 x ^{8} y ^{4}}

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What is (8xy)^{-2}*(x^{-5}y^{-1})/(xy) ?
The solution to (8xy)^{-2}*(x^{-5}y^{-1})/(xy) is 1/(64x^8y^4)