化简 468(1+(0.033)/6)^{-0.1}

解答

化简

468 (1 + \frac{0.033}{6})^{- 0.1}

\frac{468 \cdot 200 0 ^{0.1}}{201 1 ^{0.1}}

十进制

467.74337 \dots

求解步骤

468 (1 + \frac{0.033}{6})^{- 0.1}

使用指数法则:

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

(1 + \frac{0.033}{6})^{- 0.1} = \frac{1}{( 1 + \frac{0.033}{6} ) ^{0.1}}

= 468 \cdot \frac{1}{( 1 + \frac{0.033}{6} ) ^{0.1}}

(1 + \frac{0.033}{6})^{0.1} = \frac{201 1 ^{0.1}}{200 0 ^{0.1}}

= 468 \cdot \frac{1}{\frac{201 1 ^{0.1}}{200 0 ^{0.1}}}

使用分式法则:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= 468 \cdot \frac{200 0 ^{0.1}}{201 1 ^{0.1}}

468 \cdot \frac{200 0 ^{0.1}}{201 1 ^{0.1}} = \frac{468 \cdot 200 0 ^{0.1}}{201 1 ^{0.1}}

= \frac{468 \cdot 200 0 ^{0.1}}{201 1 ^{0.1}}

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