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受欢迎的代数 >

化简 (110^{-12})10^{86/10}

解答

化简

(1 \cdot 1 0^{- 12}) \cdot 1 0^{\frac{86}{10}}

解答

\frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

+1

十进制

0.00039 \dots

求解步骤

(1 \cdot 1 0^{- 12}) \cdot 1 0^{\frac{86}{10}}

使用指数法则:

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

= 1 \cdot 1 0^{\frac{86}{10}} \cdot \frac{1}{1 0 ^{12}}

1 0^{\frac{86}{10}} = 1 0^{8} \cdot 1 0^{\frac{3}{5}}

= 1 0^{8} \cdot 1 \cdot 1 0^{\frac{3}{5}} \cdot \frac{1}{1 0 ^{12}}

分解整数

10 = 2 \cdot 5

= 1 \cdot \frac{1}{1 0 ^{12}} (2 \cdot 5)^{8} \cdot 1 0^{\frac{3}{5}}

使用指数法则:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{8} = 2^{8} \cdot 5^{8}

= 1 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{8} \cdot 5^{8} \cdot 1 0^{\frac{3}{5}}

分解整数

10 = 2 \cdot 5

= 1 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{8} \cdot 5^{8} (2 \cdot 5)^{\frac{3}{5}}

使用指数法则:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{\frac{3}{5}} = 2^{\frac{3}{5}} \cdot 5^{\frac{3}{5}}

= 1 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{8} \cdot 5^{8} \cdot 2^{\frac{3}{5}} \cdot 5^{\frac{3}{5}}

使用指数法则:

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

5^{8} \cdot 5^{\frac{3}{5}} = 5^{8 + \frac{3}{5}}

= 1 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{8} \cdot 2^{\frac{3}{5}} \cdot 5^{8 + \frac{3}{5}}

5^{8 + \frac{3}{5}} = 5^{8} \cdot 5^{\frac{3}{5}}

= 2^{8} \cdot 5^{8} \cdot 1 \cdot 2^{\frac{3}{5}} \cdot 5^{\frac{3}{5}} \cdot \frac{1}{1 0 ^{12}}

分式相乘:

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

= 1 \cdot \frac{2 ^{8} \cdot 5 ^{8} \cdot 1 \cdot 2 ^{\frac{3}{5}} \cdot 5 ^{\frac{3}{5}}}{1 0 ^{12}}

\frac{1 \cdot 2 ^{8} \cdot 2 ^{\frac{3}{5}} \cdot 5 ^{8} \cdot 5 ^{\frac{3}{5}}}{1 0 ^{12}} = \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

= 1 \cdot \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

乘以:

1 \cdot \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}} = \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

= \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

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