簡約 (\sqrt[8]{16x^{12}})^6

解

簡約

(8 16 x^{12})^{6}

8 x^{9}

解答ステップ

(8 16 x^{12})^{6}

簡素化

8 16 x^{12} : 8 2^{4} x 8 x^{4}

= (8 2^{4} x 8 x^{4})^{6}

指数の規則を適用する:

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

(8 2^{4} x 8 x^{4})^{6} = (8 2^{4})^{6} x^{6} (8 x^{4})^{6}

= (8 2^{4})^{6} x^{6} (8 x^{4})^{6}

(8 2^{4})^{6} = 2^{3}

= 2^{3} x^{6} (8 x^{4})^{6}

(8 x^{4})^{6} = x^{3}

= 2^{3} x^{6} x^{3}

指数の規則を適用する:

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

x^{6} x^{3} = x^{6 + 3}

= 2^{3} x^{6 + 3}

改良

= 8 x^{9}