簡約 (3m^4n^6)(2mn)(2m^2n)

解

簡約

(3 m^{4} n^{6}) (2 mn) (2 m^{2} n)

12 m^{7} n^{8}

解答ステップ

(3 m^{4} n^{6}) (2 mn) (2 m^{2} n)

指数の規則を適用する:

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

2 \cdot 2 = 2^{1 + 1}

= 3 m^{4} n^{6} mn \cdot 2^{1 + 1} m^{2} n

数を足す:

1 + 1 = 2

= 3 m^{4} n^{6} mn \cdot 2^{2} m^{2} n

指数の規則を適用する:

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

m^{4} m m^{2} = m^{4 + 1 + 2}

= 3 n^{6} n \cdot 2^{2} m^{4 + 1 + 2} n

数を足す:

4 + 1 + 2 = 7

= 3 n^{6} n \cdot 2^{2} m^{7} n

指数の規則を適用する:

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

n^{6} nn = n^{6 + 1 + 1}

= 3 \cdot 2^{2} m^{7} n^{6 + 1 + 1}

数を足す:

6 + 1 + 1 = 8

= 3 \cdot 2^{2} m^{7} n^{8}

2^{2} = 4

= 3 \cdot 4 m^{7} n^{8}

数を乗じる:

3 \cdot 4 = 12

= 12 m^{7} n^{8}