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受欢迎的代数 >

化简 ((0.2^5)/5)4pi9*pi10^{-9}(pi/2-1/4)

解答

化简

(\frac{0. 2 ^{5}}{5}) \cdot 4 π \cdot 9 \cdot π \cdot 1 0^{- 9} \cdot (\frac{π}{2} - \frac{1}{4})

解答

3.00343 E - 11

求解步骤

(\frac{0. 2 ^{5}}{5}) \cdot 4 π 9 π 1 0^{- 9} (\frac{π}{2} - \frac{1}{4})

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

ππ = π^{1 + 1}

= \frac{0. 2 ^{5}}{5} \cdot 4 \cdot 9 π^{1 + 1} \cdot 1 0^{- 9} (\frac{π}{2} - \frac{1}{4})

数字相加:

1 + 1 = 2

= \frac{0. 2 ^{5}}{5} \cdot 4 \cdot 9 π^{2} \cdot 1 0^{- 9} (\frac{π}{2} - \frac{1}{4})

使用指数法则:

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

1 0^{- 9} = \frac{1}{1 0 ^{9}}

= 4 \cdot 9 π^{2} \frac{1}{1 0 ^{9}} \cdot \frac{0. 2 ^{5}}{5} (\frac{π}{2} - \frac{1}{4})

分式相乘:

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

= \frac{0. 2 ^{5} \cdot 1 \cdot 4 \cdot 9 π ^{2} ( \frac{π}{2} - \frac{1}{4} )}{5 \cdot 1 0 ^{9}}

数字相乘:

1 \cdot 4 \cdot 9 = 36

= \frac{36 \cdot 0. 2 ^{5} π ^{2} ( \frac{π}{2} - \frac{1}{4} )}{1 0 ^{9} \cdot 5}

分解

36 : 2^{2} \cdot 3^{2}

分解

1 0^{9} : 2^{9} \cdot 5^{9}

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 0. 2 ^{5} π ^{2} ( \frac{π}{2} - \frac{1}{4} )}{2 ^{9} \cdot 5 ^{9} \cdot 5}

5 \cdot 2^{9} \cdot 5^{9} = 2^{9} \cdot 5^{10}

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 0. 2 ^{5} π ^{2} ( \frac{π}{2} - \frac{1}{4} )}{5 ^{10} \cdot 2 ^{9}}

消掉

\frac{2 ^{2} \cdot 3 ^{2} \cdot 0. 2 ^{5} π ^{2} ( \frac{π}{2} - \frac{1}{4} )}{2 ^{9} \cdot 5 ^{10}} : \frac{3 ^{2} \cdot 0. 2 ^{5} π ^{2} ( \frac{π}{2} - \frac{1}{4} )}{5 ^{10} \cdot 2 ^{7}}

= \frac{3 ^{2} \cdot 0. 2 ^{5} π ^{2} ( \frac{π}{2} - \frac{1}{4} )}{5 ^{10} \cdot 2 ^{7}}

化简

\frac{π}{2} - \frac{1}{4} : \frac{2 π - 1}{4}

= \frac{3 ^{2} \cdot 0. 2 ^{5} π ^{2} \frac{2 π - 1}{4}}{5 ^{10} \cdot 2 ^{7}}

3^{2} \cdot 0. 2^{5} π^{2} \frac{π 2 - 1}{4} = 0.00288 π^{2} \frac{2 π - 1}{4}

= \frac{0.00288 π ^{2} \frac{2 π - 1}{4}}{5 ^{10} \cdot 2 ^{7}}

5^{10} \cdot 2^{7} = 1250000000

= \frac{0.00288 π ^{2} \frac{2 π - 1}{4}}{1250000000}

转换为小数形式

π^{2} = 9.86960 \dots

= \frac{0.00288 \cdot 9.86960 \dots \cdot \frac{2 π - 1}{4}}{1250000000}

数字相乘:

0.00288 \cdot 9.86960 \dots = 0.02842 \dots

= \frac{0.02842 \dots \cdot \frac{2 π - 1}{4}}{1250000000}

数字相除:

\frac{0.02842 \dots}{1250000000} = 2.27396 E - 11

= 2.27396 E - 11 \cdot \frac{2 π - 1}{4}

分式相乘:

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

= \frac{( π 2 - 1 ) \cdot 2.27396 E - 11}{4}

数字相除:

\frac{2.27396 E - 11}{4} = 5.68489 E - 12

= 5.68489 E - 12 (2 π - 1)

使用分配律:

a (b - c) = ab - a c

a = 5.68489 E - 12, b = π 2, c = 1

= 5.68489 E - 12 π 2 - 5.68489 E - 12 \cdot 1

= 2 \cdot 5.68489 E - 12 π - 1 \cdot 5.68489 E - 12

化简

2 \cdot 5.68489 E - 12 π - 1 \cdot 5.68489 E - 12 : 3.00343 E - 11

= 3.00343 E - 11

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