簡約 (sqrt(x^2+a^2))^{e^{x^2}}

解

簡約

(x^{2} + a^{2})^{e^{x^{2}}}

(x^{2} + a^{2})^{\frac{e ^{x^{2}}}{2}}

解答ステップ

(x^{2} + a^{2})^{e^{x^{2}}}

累乗根の規則を適用する:

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

= ((x^{2} + a^{2})^{\frac{1}{2}})^{e^{x^{2}}}

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} + a^{2})^{\frac{1}{2} e^{x^{2}}}

簡素化

\frac{1}{2} e^{x^{2}} : \frac{e ^{x^{2}}}{2}

= (x^{2} + a^{2})^{\frac{e ^{x^{2}}}{2}}