簡約 1.983^{14}*1983^{-6}

解

簡約

1.98 3^{14} \cdot 198 3^{- 6}

\frac{2.52404 E 13}{66 1 ^{6} \cdot 1265625000000}

十進法表記

2.39101 E - 16

解答ステップ

1.98 3^{14} \cdot 198 3^{- 6}

1.98 3^{14} = 14538.44637 \dots

= 14538.44637 \dots \cdot 198 3^{- 6}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

198 3^{- 6} = \frac{1}{198 3 ^{6}}

= 14538.44637 \dots \cdot \frac{1}{198 3 ^{6}}

14538.44637 \dots \cdot \frac{1}{198 3 ^{6}} = \frac{14538.44637 \dots}{198 3 ^{6}}

= \frac{14538.44637 \dots}{198 3 ^{6}}

\frac{14538.44637 \dots}{198 3 ^{6}} = \frac{1.45384 E 16}{1000000000000 \cdot 198 3 ^{6}}

= \frac{1.45384 E 16}{1000000000000 \cdot 198 3 ^{6}}

数を因数に分解する:

1.45384 E 16 = 64 \cdot 2.27163 E 14

= \frac{64 \cdot 2.27163 E 14}{1000000000000 \cdot 198 3 ^{6}}

数を因数に分解する:

1000000000000 = 64 \cdot 15625000000

= \frac{64 \cdot 2.27163 E 14}{64 \cdot 15625000000 \cdot 198 3 ^{6}}

共通因数を約分する:

64

= \frac{2.27163 E 14}{15625000000 \cdot 198 3 ^{6}}

因数

2.27163 E 14 : 3^{2} \cdot 2.52404 E 13

= \frac{3 ^{2} \cdot 2.52404 E 13}{15625000000 \cdot 198 3 ^{6}}

因数

198 3^{6} : 3^{6} \cdot 66 1^{6}

= \frac{3 ^{2} \cdot 2.52404 E 13}{15625000000 \cdot 3 ^{6} \cdot 66 1 ^{6}}

\frac{3 ^{2}}{3 ^{6}} = \frac{1}{3 ^{4}}

= \frac{2.52404 E 13}{15625000000 \cdot 3 ^{4} \cdot 66 1 ^{6}}

15625000000 \cdot 3^{4} \cdot 66 1^{6} = 66 1^{6} \cdot 1265625000000

= \frac{2.52404 E 13}{66 1 ^{6} \cdot 1265625000000}