What is m^{19}n^{19}(1/m)^{30}(1/n)^{30} ?

The solution to m^{19}n^{19}(1/m)^{30}(1/n)^{30} is 1/(m^{11)n^{11}}

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simplify m^{19}n^{19}(1/m)^{30}(1/n)^{30}

simplify

m^{19} n^{19} (\frac{1}{m})^{30} (\frac{1}{n})^{30}

\frac{1}{m ^{11} n ^{11}}

Solution steps

m^{19} n^{19} (\frac{1}{m})^{30} (\frac{1}{n})^{30}

Simplify

(\frac{1}{m})^{30} : \frac{1}{m ^{30}}

= m^{19} n^{19} \frac{1}{m ^{30}} (\frac{1}{n})^{30}

Simplify

(\frac{1}{n})^{30} : \frac{1}{n ^{30}}

= m^{19} n^{19} \frac{1}{m ^{30}} \cdot \frac{1}{n ^{30}}

Apply the fraction rule:

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

= \frac{m ^{19} n ^{19} \cdot 1 \cdot 1}{m ^{30} n ^{30}}

Simplify

m^{19} n^{19} \cdot 1 \cdot 1 : m^{19} n^{19}

= \frac{m ^{19} n ^{19}}{m ^{30} n ^{30}}

Simplify

\frac{m ^{19}}{m ^{30}} : \frac{1}{m ^{11}}

= \frac{n ^{19}}{m ^{11} n ^{30}}

Simplify

\frac{n ^{19}}{n ^{30}} : \frac{1}{n ^{11}}

= \frac{1}{m ^{11} n ^{11}}

2 \cdot \frac{7}{2}

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

\frac{8 x ^{2}}{16 x ^{4} + 144 x ^{3}}

2 + 2 + 2

(x^{2} y^{5})^{3}

What is m^{19}n^{19}(1/m)^{30}(1/n)^{30} ?
The solution to m^{19}n^{19}(1/m)^{30}(1/n)^{30} is 1/(m^{11)n^{11}}