簡約 \sqrt[3]{54.22}^2

解

簡約

3 54.22^{2}

\frac{3 7349521}{5 3 20}

十進法表記

14.32538 \dots

解答ステップ

(3 54.22)^{2}

54.22 = \frac{2711}{50}

= (3 \frac{2711}{50})^{2}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

= ((\frac{2711}{50})^{\frac{1}{3}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (\frac{2711}{50})^{\frac{1}{3} \cdot 2}

\frac{1}{3} \cdot 2 = \frac{2}{3}

= (\frac{2711}{50})^{\frac{2}{3}}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{271 1 ^{\frac{2}{3}}}{5 0 ^{\frac{2}{3}}}

同じべき乗を組み合わせる :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = m \frac{x ^{a}}{y ^{b}}

= 3 \frac{271 1 ^{2}}{5 0 ^{2}}

\frac{271 1 ^{2}}{5 0 ^{2}} = \frac{7349521}{2500}

= 3 \frac{7349521}{2500}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{3 7349521}{3 2500}

32500 = 5320

= \frac{3 7349521}{5 3 20}