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受欢迎的代数 >

化简 (\sqrt[3]{(12w)})^5

解答

化简

(3 (12 w))^{5}

解答

12 3 1 2^{2} 3 w^{5}

求解步骤

(3 12 w)^{5}

使用法则:

(a) = a

(12 w) = 12 w

= (3 12 w)^{5}

使用指数法则:

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

(3 12 w)^{3 + 2} = (3 12 w)^{3} (3 12 w)^{2}

= (3 12 w)^{3} (3 12 w)^{2}

使用指数法则:

(n a)^{n} = a,

假定

n i s o dd or a \geq 0

(3 12 w)^{3} = 12 w

= 12 w (3 12 w)^{2}

(3 12 w)^{2} = 1 2^{\frac{2}{3}} (3 w)^{2}

= 12 \cdot 1 2^{\frac{2}{3}} w (3 w)^{2}

使用指数法则:

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

12 \cdot 1 2^{\frac{2}{3}} = 1 2^{1 + \frac{2}{3}}

= w \cdot 1 2^{1 + \frac{2}{3}} (3 w)^{2}

1 2^{1 + \frac{2}{3}} = 12 \cdot 1 2^{\frac{2}{3}}

= 12 \cdot 1 2^{\frac{2}{3}} w (3 w)^{2}

= 1 2^{\frac{2}{3}} \cdot 12 w (3 w)^{2}

化简

w (3 w)^{2} : w^{\frac{5}{3}}

= 1 2^{\frac{2}{3}} \cdot 12 w^{\frac{5}{3}}

1 2^{\frac{2}{3}} \cdot 12 = 1 2^{\frac{5}{3}}

= 1 2^{\frac{5}{3}} w^{\frac{5}{3}}

1 2^{\frac{5}{3}} = 12 \cdot 1 2^{\frac{2}{3}}

= 12 \cdot 1 2^{\frac{2}{3}} w^{\frac{5}{3}}

1 2^{\frac{2}{3}} = 3 1 2^{2}

= 12 3 1 2^{2} 3 w^{5}

w^{\frac{5}{3}} = 3 w^{5}

= 12 3 1 2^{2} 3 w^{5}

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