簡約 (5.196)^2((4.500026+1.5)/2)^{-3}

解

簡約

(5.196)^{2} (\frac{4.500026 + 1.5}{2})^{- 3}

0.99992 \dots

解答ステップ

(5.196)^{2} (\frac{4.500026 + 1.5}{2})^{- 3}

指数の規則を適用する:

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

= 5.19 6^{2} \cdot \frac{1}{( \frac{1.5 + 4.500026}{2} ) ^{3}}

\frac{1}{( \frac{4.500026 + 1.5}{2} ) ^{3}} = \frac{2 ^{3}}{6.00002 6 ^{3}}

= 5.19 6^{2} \cdot \frac{2 ^{3}}{6.00002 6 ^{3}}

分数を乗じる:

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

= \frac{2 ^{3} \cdot 5.19 6 ^{2}}{6.00002 6 ^{3}}

2^{3} \cdot 5.19 6^{2} = 215.987328

= \frac{215.987328}{6.00002 6 ^{3}}

6.00002 6^{3} = 216.00280 \dots

= \frac{215.987328}{216.00280 \dots}

数を割る:

\frac{215.987328}{216.00280 \dots} = 0.99992 \dots

= 0.99992 \dots