What is 8(x^2y^{-1})^{-4} ?

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

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simplify 8(x^2y^{-1})^{-4}

simplify

8 (x^{2} y^{- 1})^{- 4}

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

Solution steps

8 (x^{2} y^{- 1})^{- 4}

Apply exponent rule:

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

(x^{2} y^{- 1})^{- 4} = \frac{1}{( x ^{2} y ^{- 1} ) ^{4}}

= 8 \cdot \frac{1}{( x ^{2} y ^{- 1} ) ^{4}}

Simplify

(x^{2} y^{- 1})^{4} : \frac{x ^{8}}{y ^{4}}

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

Apply the fraction rule:

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

= 8 \cdot \frac{y ^{4}}{x ^{8}}

Apply the fraction rule:

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

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

\frac{35}{15}

b^{2} (12 b - 1)

81 x^{12}

64 + 8

e^{0} + 1