簡約 (49m^4n-21m^6n^2)/(7m^2n^4)

解

簡約

\frac{49 m ^{4} n - 21 m ^{6} n ^{2}}{7 m ^{2} n ^{4}}

\frac{m ^{2} ( 7 - 3 m ^{2} n )}{n ^{3}}

解答ステップ

\frac{49 m ^{4} n - 21 m ^{6} n ^{2}}{7 m ^{2} n ^{4}}

因数

49 m^{4} n - 21 m^{6} n^{2} : 7 m^{4} n (7 - 3 m^{2} n)

= \frac{7 m ^{4} n ( 7 - 3 m ^{2} n )}{7 m ^{2} n ^{4}}

共通因数を約分する:

7

= \frac{m ^{4} n ( 7 - 3 m ^{2} n )}{m ^{2} n ^{4}}

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

m^{4} = m^{2} m^{2}

= \frac{m ^{2} m ^{2} n ( 7 - 3 m ^{2} n )}{m ^{2} n ^{4}}

共通因数を約分する:

m^{2}

= \frac{m ^{2} n ( 7 - 3 m ^{2} n )}{n ^{4}}

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

n^{4} = n n^{3}

= \frac{m ^{2} n ( 7 - 3 m ^{2} n )}{n n ^{3}}

共通因数を約分する:

n

= \frac{m ^{2} ( 7 - 3 m ^{2} n )}{n ^{3}}