簡約 5((5^3)/(2/5))^2

解

簡約

5 (\frac{5 ^{3}}{\frac{2}{5}})^{2}

\frac{1953125}{4}

十進法表記

488281.25

解答ステップ

5 (\frac{5 ^{3}}{\frac{2}{5}})^{2}

指数の規則を適用する:

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

(\frac{5 ^{3}}{\frac{2}{5}})^{2} = \frac{( 5 ^{3} ) ^{2}}{( \frac{2}{5} ) ^{2}}

= 5 \cdot \frac{( 5 ^{3} ) ^{2}}{( \frac{2}{5} ) ^{2}}

(5^{3})^{2} = 15625

= 5 \cdot \frac{15625}{( \frac{2}{5} ) ^{2}}

(\frac{2}{5})^{2} = \frac{4}{25}

= 5 \cdot \frac{15625}{\frac{4}{25}}

\frac{15625}{\frac{4}{25}} = \frac{390625}{4}

= 5 \cdot \frac{390625}{4}

5 \cdot \frac{390625}{4} = \frac{1953125}{4}

= \frac{1953125}{4}