化简 (6^{1/2}*4^{1/3})^2

解答

化简

(6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}})^{2}

6 \cdot 4^{\frac{2}{3}}

十进制

15.11905 \dots

求解步骤

(6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}})^{2}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

(6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}})^{2} = (6^{\frac{1}{2}})^{2} (4^{\frac{1}{3}})^{2}

= (6^{\frac{1}{2}})^{2} (4^{\frac{1}{3}})^{2}

(6^{\frac{1}{2}})^{2} = 6

= 6 (4^{\frac{1}{3}})^{2}

使用指数法则:

(a^{b})^{c} = a^{b c}, a \geq 0

(4^{\frac{1}{3}})^{2} = 4^{\frac{1}{3} \cdot 2}

= 6 \cdot 4^{\frac{1}{3} \cdot 2}

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

= 6 \cdot 4^{\frac{2}{3}}

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