簡約 m^{19}n^{19}(1/m)^{30}(1/n)^{30}

解

簡約

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

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

解答ステップ

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

簡素化

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

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

簡素化

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

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

分数の規則を適用する:

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}}

簡素化

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

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

簡素化

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

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

簡素化

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

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