簡約 (2^3x^2)^5

解

簡約

(2^{3} x^{2})^{5}

32768 x^{10}

解答ステップ

(2^{3} x^{2})^{5}

指数の規則を適用する:

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

(2^{3} x^{2})^{5} = (2^{3})^{5} (x^{2})^{5}

= (2^{3})^{5} (x^{2})^{5}

(2^{3})^{5} = 32768

= 32768 (x^{2})^{5}

指数の規則を適用する:

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

, 以下を想定

a \geq 0

(x^{2})^{5} = x^{2 \cdot 5}

= 32768 x^{2 \cdot 5}

数を乗じる:

2 \cdot 5 = 10

= 32768 x^{10}