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受欢迎的代数 >

化简 \sqrt[5]{8}^{a+3}*\sqrt[5]{4x}^{2-a}

解答

化简

58^{a + 3} \cdot 5 4 x^{2 - a}

解答

2^{\frac{a + 13}{5}} x^{\frac{- a + 2}{5}}

求解步骤

(58)^{a + 3} (5 4 x)^{2 - a}

(58)^{a + 3} : 8^{\frac{a + 3}{5}}

= 8^{\frac{a + 3}{5}} (5 4 x)^{2 - a}

(5 4 x)^{2 - a} : (4 x)^{\frac{2 - a}{5}}

= 8^{\frac{a + 3}{5}} (4 x)^{\frac{2 - a}{5}}

(4 x)^{\frac{2 - a}{5}} = 4^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

= 8^{\frac{a + 3}{5}} \cdot 4^{\frac{- a + 2}{5}} x^{\frac{- a + 2}{5}}

分解整数

8 = 2^{3}

= (2^{3})^{\frac{a + 3}{5}} \cdot 4^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

使用指数法则:

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

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

= 2^{3 \cdot \frac{a + 3}{5}} \cdot 4^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

整理后得

= 2^{\frac{3 ( a + 3 )}{5}} \cdot 4^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

分解整数

4 = 2^{2}

= 2^{\frac{3 ( a + 3 )}{5}} (2^{2})^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

使用指数法则:

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

(2^{2})^{\frac{2 - a}{5}} = 2^{2 \cdot \frac{2 - a}{5}}

= 2^{\frac{3 ( a + 3 )}{5}} \cdot 2^{2 \cdot \frac{2 - a}{5}} x^{\frac{2 - a}{5}}

整理后得

= 2^{\frac{3 ( a + 3 )}{5}} \cdot 2^{\frac{2 ( 2 - a )}{5}} x^{\frac{2 - a}{5}}

使用指数法则:

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

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

= 2^{\frac{3 ( a + 3 )}{5} + \frac{2 ( 2 - a )}{5}} x^{\frac{2 - a}{5}}

使用法则

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

= 2^{\frac{3 ( a + 3 ) + 2 ( 2 - a )}{5}} x^{\frac{2 - a}{5}}

2^{\frac{3 ( a + 3 ) + 2 ( 2 - a )}{5}} = 2^{\frac{a + 13}{5}}

= 2^{\frac{a + 13}{5}} x^{\frac{- a + 2}{5}}

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