簡約 4piar^2((1/2)^{1/4}(z/r)^{1/2}T)*T^4

解

簡約

4 πa r^{2} \cdot ((\frac{1}{2})^{\frac{1}{4}} (\frac{z}{r})^{\frac{1}{2}} \cdot T) \cdot T^{4}

4 π (\frac{1}{2})^{\frac{1}{4}} a r^{2} (\frac{z}{r})^{\frac{1}{2}} T^{5}

解答ステップ

4 πa r^{2} ((\frac{1}{2})^{\frac{1}{4}} (\frac{z}{r})^{\frac{1}{2}} T) T^{4}

指数の規則を適用する:

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

T T^{4} = T^{1 + 4}

= 4 πa r^{2} (\frac{1}{2})^{\frac{1}{4}} (\frac{z}{r})^{\frac{1}{2}} T^{1 + 4}

数を足す:

1 + 4 = 5

= 4 πa r^{2} (\frac{1}{2})^{\frac{1}{4}} (\frac{z}{r})^{\frac{1}{2}} T^{5}