What is mn(m^{-2}n^2)(m^2n^{-2}) ?

The solution to mn(m^{-2}n^2)(m^2n^{-2}) is mn

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simplify mn(m^{-2}n^2)(m^2n^{-2})

simplify

mn (m^{- 2} n^{2}) (m^{2} n^{- 2})

mn

Solution steps

mn (m^{- 2} n^{2}) (m^{2} n^{- 2})

Simplify

m^{- 2} n^{2} : \frac{n ^{2}}{m ^{2}}

= mn \frac{n ^{2}}{m ^{2}} m^{2} n^{- 2}

Apply exponent rule:

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

n^{- 2} = \frac{1}{n ^{2}}

= mn \frac{n ^{2}}{m ^{2}} m^{2} \frac{1}{n ^{2}}

Simplify

m m^{2} : m^{3}

= m^{3} n \frac{n ^{2}}{m ^{2}} \cdot \frac{1}{n ^{2}}

Cross-cancel common factor:

n^{2}

= m^{3} n \frac{1}{m ^{2}}

Apply the fraction rule:

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

= \frac{m ^{3} n \cdot 1}{m ^{2}}

Apply rule:

a \cdot 1 = a

m^{3} n \cdot 1 = m^{3} n

= \frac{m ^{3} n}{m ^{2}}

Simplify

\frac{m ^{3}}{m ^{2}} : m

= mn

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What is mn(m^{-2}n^2)(m^2n^{-2}) ?
The solution to mn(m^{-2}n^2)(m^2n^{-2}) is mn