簡約 (6.3)(1/3)^3(2/3)^3

解

簡約

(6.3) (\frac{1}{3})^{3} (\frac{2}{3})^{3}

\frac{28}{405}

十進法表記

0.06913 \dots

解答ステップ

(6.3) (\frac{1}{3})^{3} (\frac{2}{3})^{3}

規則を適用する:

(a) = a

(6.3) = 6.3

= 6.3 (\frac{1}{3})^{3} (\frac{2}{3})^{3}

(\frac{1}{3})^{3} = \frac{1}{27}

= 6.3 \cdot \frac{1}{27} (\frac{2}{3})^{3}

指数の規則を適用する:

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

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

= 6.3 \cdot \frac{1}{27} \cdot \frac{2 ^{3}}{3 ^{3}}

2^{3} = 8

= 6.3 \cdot \frac{1}{27} \cdot \frac{8}{3 ^{3}}

3^{3} = 27

= 6.3 \cdot \frac{1}{27} \cdot \frac{8}{27}

6.3 = \frac{63}{10}

= \frac{63}{10} \cdot \frac{1}{27} \cdot \frac{8}{27}

\frac{63}{10} \cdot \frac{1}{27} \cdot \frac{8}{27} = \frac{28}{405}

= \frac{28}{405}