簡約 (3a^3b^{-1}a)^2

解

簡約

(3 a^{3} b^{- 1} a)^{2}

\frac{9 a ^{8}}{b ^{2}}

解答ステップ

(3 a^{3} b^{- 1} a)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(3 a^{3} b^{- 1} a)^{2} = 3^{2} (a^{3})^{2} (b^{- 1})^{2} a^{2}

= 3^{2} (a^{3})^{2} (b^{- 1})^{2} a^{2}

3^{2} = 9

= 9 (a^{3})^{2} (b^{- 1})^{2} a^{2}

簡素化

(a^{3})^{2} : a^{6}

= 9 a^{6} (b^{- 1})^{2} a^{2}

簡素化

(b^{- 1})^{2} : \frac{1}{b ^{2}}

= 9 a^{6} \frac{1}{b ^{2}} a^{2}

指数の規則を適用する:

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

a^{6} a^{2} = a^{6 + 2}

= 9 \cdot \frac{1}{b ^{2}} a^{6 + 2}

数を足す:

6 + 2 = 8

= 9 \cdot \frac{1}{b ^{2}} a^{8}

分数を乗じる:

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

= \frac{1 \cdot 9 a ^{8}}{b ^{2}}

数を乗じる:

1 \cdot 9 = 9

= \frac{9 a ^{8}}{b ^{2}}