簡約-(5*10^{-6})((13.5721)/(5.21))^{3/2}

解

簡約

- (5 \cdot 1 0^{- 6}) (\frac{13.5721}{5.21})^{\frac{3}{2}}

- \frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{52 1 ^{\frac{1}{2}} \cdot 104200000000}

十進法表記

- 0.00002 \dots

解答ステップ

- (5 \cdot 1 0^{- 6}) (\frac{13.5721}{5.21})^{\frac{3}{2}}

簡素化

5 \cdot 1 0^{- 6} : \frac{1}{200000}

= - \frac{1}{200000} (\frac{13.5721}{5.21})^{\frac{3}{2}}

指数の規則を適用する:

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

(\frac{13.5721}{5.21})^{\frac{3}{2}} = \frac{13.572 1 ^{\frac{3}{2}}}{5.2 1 ^{\frac{3}{2}}}

= - \frac{1}{200000} \cdot \frac{13.572 1 ^{\frac{3}{2}}}{5.2 1 ^{\frac{3}{2}}}

13.572 1^{\frac{3}{2}} = \frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{1000000}

= - \frac{1}{200000} \cdot \frac{\frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{1000000}}{5.2 1 ^{\frac{3}{2}}}

5.2 1^{\frac{3}{2}} = \frac{521 \cdot 52 1 ^{\frac{1}{2}}}{1000}

= - \frac{1}{200000} \cdot \frac{\frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{1000000}}{\frac{521 \cdot 52 1 ^{\frac{1}{2}}}{1000}}

\frac{\frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{1000000}}{\frac{521 \cdot 52 1 ^{\frac{1}{2}}}{1000}} = \frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{521000 \cdot 52 1 ^{\frac{1}{2}}}

= - \frac{1}{200000} \cdot \frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{521000 \cdot 52 1 ^{\frac{1}{2}}}

- \frac{1}{200000} \cdot \frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{521000 \cdot 52 1 ^{\frac{1}{2}}} = - \frac{13572 1 ^{\frac{1}{2}} \cdot 135721}{52 1 ^{\frac{1}{2}} \cdot 104200000000}

= - \frac{13572 1 ^{\frac{1}{2}} \cdot 135721}{52 1 ^{\frac{1}{2}} \cdot 104200000000}

13572 1^{\frac{1}{2}} \cdot 135721 = 135721 \cdot 13572 1^{\frac{1}{2}}

= - \frac{135721 \cdot 13572 1 ^{\frac{1}{2}}}{52 1 ^{\frac{1}{2}} \cdot 104200000000}