簡約 (3^x+3^x)^2

解

簡約

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

4 \cdot 9^{x}

解答ステップ

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

類似した元を足す:

3^{x} + 3^{x} = 2 \cdot 3^{x}

= (2 \cdot 3^{x})^{2}

指数の規則を適用する:

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

(2 \cdot 3^{x})^{2} = 2^{2} (3^{x})^{2}

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

2^{2} = 4

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

指数の規則を適用する:

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

(3^{x})^{2} = 3^{x \cdot 2}

= 4 \cdot 3^{x \cdot 2}

簡素化

3^{x \cdot 2} : 9^{x}

= 4 \cdot 9^{x}