What is (2^{-2}x^{-3}y^{-4})^{-1} ?

The solution to (2^{-2}x^{-3}y^{-4})^{-1} is 4x^3y^4

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simplify (2^{-2}x^{-3}y^{-4})^{-1}

simplify

(2^{- 2} x^{- 3} y^{- 4})^{- 1}

4 x^{3} y^{4}

Solution steps

(2^{- 2} x^{- 3} y^{- 4})^{- 1}

Apply exponent rule:

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

(2^{- 2} x^{- 3} y^{- 4})^{- 1} = \frac{1}{2 ^{- 2} x ^{- 3} y ^{- 4}}

= \frac{1}{2 ^{- 2} x ^{- 3} y ^{- 4}}

Multiply

2^{- 2} x^{- 3} y^{- 4} : \frac{1}{4 x ^{3} y ^{4}}

= \frac{1}{\frac{1}{4 x ^{3} y ^{4}}}

Apply the fraction rule:

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

= \frac{4 x ^{3} y ^{4}}{1}

Apply rule

\frac{a}{1} = a

= 4 x^{3} y^{4}

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What is (2^{-2}x^{-3}y^{-4})^{-1} ?
The solution to (2^{-2}x^{-3}y^{-4})^{-1} is 4x^3y^4