化简 (6x^{4/5}y^{3/5})(5xy^{3/4})

解答

化简

(6 x^{\frac{4}{5}} y^{\frac{3}{5}}) (5 x y^{\frac{3}{4}})

30 x^{\frac{9}{5}} y^{\frac{27}{20}}

求解步骤

(6 x^{\frac{4}{5}} y^{\frac{3}{5}}) (5 x y^{\frac{3}{4}})

使用指数法则:

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

y^{\frac{3}{5}} y^{\frac{3}{4}} = y^{\frac{3}{5} + \frac{3}{4}}

= 6 x^{\frac{4}{5}} \cdot 5 x y^{\frac{3}{5} + \frac{3}{4}}

y^{\frac{3}{5} + \frac{3}{4}} = y^{\frac{27}{20}}

= 6 \cdot 5 x x^{\frac{4}{5}} y^{\frac{27}{20}}

数字相乘:

6 \cdot 5 = 30

= 30 x x^{\frac{4}{5}} y^{\frac{27}{20}}

使用指数法则:

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

x^{\frac{4}{5}} x = x^{\frac{4}{5} + 1}

= 30 x^{\frac{4}{5} + 1} y^{\frac{27}{20}}

x^{\frac{4}{5} + 1} = x^{\frac{9}{5}}

= 30 x^{\frac{9}{5}} y^{\frac{27}{20}}

s im pl i f y (3 \frac{27 x}{x y ^{3}})^{3}

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