化简 (4/5)^3(3/10)^{-2}(4/3)^{-4}

解答

化简

(\frac{4}{5})^{3} \cdot (\frac{3}{10})^{- 2} \cdot (\frac{4}{3})^{- 4}

\frac{9}{5}

十进制

1.8

求解步骤

(\frac{4}{5})^{3} (\frac{3}{10})^{- 2} (\frac{4}{3})^{- 4}

(\frac{4}{5})^{3} = \frac{64}{125}

= \frac{64}{125} (\frac{3}{10})^{- 2} (\frac{4}{3})^{- 4}

(\frac{3}{10})^{- 2} = \frac{100}{9}

= \frac{64}{125} \cdot \frac{100}{9} (\frac{4}{3})^{- 4}

使用指数法则:

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

(\frac{4}{3})^{- 4} = \frac{1}{( \frac{4}{3} ) ^{4}}

= \frac{64}{125} \cdot \frac{100}{9} \cdot \frac{1}{( \frac{4}{3} ) ^{4}}

(\frac{4}{3})^{4} = \frac{256}{81}

= \frac{64}{125} \cdot \frac{100}{9} \cdot \frac{1}{\frac{256}{81}}

使用分式法则:

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

= \frac{64}{125} \cdot \frac{100}{9} \cdot \frac{81}{256}

\frac{64}{125} \cdot \frac{100}{9} \cdot \frac{81}{256} = \frac{9}{5}

= \frac{9}{5}

r a t i o na l i ze d e n o mina t or \frac{6}{11 + 3}

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- 4 \div \frac{1}{2}

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s im pl i f y (2 x - 1) (x + 4) - (2 x - 1) (3 x + 1)