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受欢迎的代数 >

化简 1/2 (5010^{-3})((2pi0.17)/(1.8))^2

解答

化简

\frac{1}{2} (50 \cdot 1 0^{- 3}) (\frac{2 π \cdot 0.17}{1.8})^{2}

解答

0.00880 \dots

求解步骤

\frac{1}{2} (50 \cdot 1 0^{- 3}) (\frac{2 π 0.17}{1.8})^{2}

使用指数法则:

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

= 50 \cdot \frac{1}{2} \cdot \frac{1}{1 0 ^{3}} (\frac{2 \cdot 0.17 π}{1.8})^{2}

(\frac{2 π 0.17}{1.8})^{2} = \frac{0.3 4 ^{2} π ^{2}}{1. 8 ^{2}}

= 50 \cdot \frac{1}{2} \cdot \frac{1}{1 0 ^{3}} \cdot \frac{0.3 4 ^{2} π ^{2}}{1. 8 ^{2}}

分式相乘:

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

= \frac{1 \cdot 1 \cdot 0.3 4 ^{2} π ^{2} \cdot 50}{2 \cdot 1 0 ^{3} \cdot 1. 8 ^{2}}

数字相乘:

1 \cdot 1 \cdot 50 = 50

= \frac{50 \cdot 0.3 4 ^{2} π ^{2}}{1 0 ^{3} \cdot 2 \cdot 1. 8 ^{2}}

数字相除:

\frac{50}{2} = 25

= \frac{25 \cdot 0.3 4 ^{2} π ^{2}}{1 0 ^{3} \cdot 1. 8 ^{2}}

分解

25 : 5^{2}

分解

1 0^{3} : 2^{3} \cdot 5^{3}

= \frac{5 ^{2} \cdot 0.3 4 ^{2} π ^{2}}{2 ^{3} \cdot 5 ^{3} \cdot 1. 8 ^{2}}

消掉

\frac{5 ^{2} \cdot 0.3 4 ^{2} π ^{2}}{2 ^{3} \cdot 5 ^{3} \cdot 1. 8 ^{2}} : \frac{0.3 4 ^{2} π ^{2}}{2 ^{3} \cdot 5 \cdot 1. 8 ^{2}}

= \frac{0.3 4 ^{2} π ^{2}}{2 ^{3} \cdot 5 \cdot 1. 8 ^{2}}

0.3 4^{2} = 0.1156

= \frac{0.1156 π ^{2}}{2 ^{3} \cdot 5 \cdot 1. 8 ^{2}}

2^{3} \cdot 5 \cdot 1. 8^{2} = 129.6

= \frac{0.1156 π ^{2}}{129.6}

转换为小数形式

π^{2} = 9.86960 \dots

= \frac{0.1156 \cdot 9.86960 \dots}{129.6}

数字相乘:

0.1156 \cdot 9.86960 \dots = 1.14092 \dots

= \frac{1.14092 \dots}{129.6}

数字相除:

\frac{1.14092 \dots}{129.6} = 0.00880 \dots

= 0.00880 \dots

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