簡約 (((1.95996))/((0.005)))^20.50.5

解

簡約

(\frac{( 1.95996 )}{( 0.005 )})^{2} \cdot 0.5 \cdot 0.5

\frac{2400902001}{62500}

十進法表記

38414.432016

解答ステップ

(\frac{1.95996}{0.005})^{2} \cdot 0.5 \cdot 0.5

数を乗じる:

0.5 \cdot 0.5 = 0.25

= (\frac{1.95996}{0.005})^{2} \cdot 0.25

= 0.25 (\frac{1.95996}{0.005})^{2}

指数の規則を適用する:

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

(\frac{1.95996}{0.005})^{2} = \frac{1.9599 6 ^{2}}{0.00 5 ^{2}}

= 0.25 \cdot \frac{1.9599 6 ^{2}}{0.00 5 ^{2}}

1.9599 6^{2} = 3.84144 \dots

= 0.25 \cdot \frac{3.84144 \dots}{0.00 5 ^{2}}

0.00 5^{2} = 0.000025

= 0.25 \cdot \frac{3.84144 \dots}{0.000025}

\frac{3.84144 \dots}{0.000025} = \frac{38414432016}{250000}

= 0.25 \cdot \frac{38414432016}{250000}

数を因数に分解する:

38414432016 = 16 \cdot 2400902001

= 0.25 \cdot \frac{16 \cdot 2400902001}{250000}

数を因数に分解する:

250000 = 16 \cdot 15625

= 0.25 \cdot \frac{16 \cdot 2400902001}{16 \cdot 15625}

共通因数を約分する:

16

= 0.25 \cdot \frac{2400902001}{15625}

0.25 = \frac{1}{4}

= \frac{1}{4} \cdot \frac{2400902001}{15625}

\frac{1}{4} \cdot \frac{2400902001}{15625} = \frac{2400902001}{62500}

= \frac{2400902001}{62500}