簡約 1/(2.27)*(1.98^2)/(1.14^2)

解

簡約

\frac{1}{2.27} \cdot \frac{1.9 8 ^{2}}{1.1 4 ^{2}}

1.32890 \dots

解答ステップ

\frac{1}{2.27} \cdot \frac{1.9 8 ^{2}}{1.1 4 ^{2}}

指数の規則を適用する:

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

\frac{1.9 8 ^{2}}{1.1 4 ^{2}} = (\frac{1.98}{1.14})^{2}

= \frac{1}{2.27} (\frac{1.98}{1.14})^{2}

(\frac{1.98}{1.14})^{2} = \frac{1.9 8 ^{2}}{1.1 4 ^{2}}

= \frac{1}{2.27} \cdot \frac{1.9 8 ^{2}}{1.1 4 ^{2}}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1.9 8 ^{2}}{2.27 \cdot 1.1 4 ^{2}}

乗算:

1 \cdot 1.9 8^{2} = 1.9 8^{2}

= \frac{1.9 8 ^{2}}{1.1 4 ^{2} \cdot 2.27}

1.9 8^{2} = 3.9204

= \frac{3.9204}{1.1 4 ^{2} \cdot 2.27}

2.27 \cdot 1.1 4^{2} = 2.950092

= \frac{3.9204}{2.950092}

数を割る:

\frac{3.9204}{2.950092} = 1.32890 \dots

= 1.32890 \dots