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人気のある代数 >

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

解

簡約

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

解

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

解答ステップ

(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}}

整数を因数分解する

8 = 2^{3}

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

指数の規則を適用する:

(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}}

改良

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

整数を因数分解する

4 = 2^{2}

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

指数の規則を適用する:

(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}}

改良

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

指数の規則を適用する:

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}}

規則を適用

\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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