化简 (2/3 x^4-1/5 y^5)^2(2/3 x^4+1/5 y^5)^2

解答

化简

(\frac{2}{3} x^{4} - \frac{1}{5} y^{5})^{2} (\frac{2}{3} x^{4} + \frac{1}{5} y^{5})^{2}

(\frac{2 x ^{4}}{3} - \frac{y ^{5}}{5})^{2} (\frac{2 x ^{4}}{3} + \frac{y ^{5}}{5})^{2}

求解步骤

(\frac{2}{3} x^{4} - \frac{1}{5} y^{5})^{2} (\frac{2}{3} x^{4} + \frac{1}{5} y^{5})^{2}

使用指数法则:

a^{m} b^{m} = (ab)^{m},

假定

a \geq 0, b \geq 0

(\frac{2}{3} x^{4} - \frac{1}{5} y^{5})^{2} (\frac{2}{3} x^{4} + \frac{1}{5} y^{5})^{2} = ((\frac{2}{3} x^{4} - \frac{1}{5} y^{5}) (\frac{2}{3} x^{4} + \frac{1}{5} y^{5}))^{2}

= ((\frac{2}{3} x^{4} - \frac{1}{5} y^{5}) (\frac{2}{3} x^{4} + \frac{1}{5} y^{5}))^{2}

化简

(\frac{2}{3} x^{4} - \frac{1}{5} y^{5}) (\frac{2}{3} x^{4} + \frac{1}{5} y^{5}) : (\frac{2 x ^{4}}{3} - \frac{y ^{5}}{5}) (\frac{2 x ^{4}}{3} + \frac{y ^{5}}{5})

= ((\frac{2 x ^{4}}{3} - \frac{y ^{5}}{5}) (\frac{2 x ^{4}}{3} + \frac{y ^{5}}{5}))^{2}

使用指数法则:

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

= (\frac{2 x ^{4}}{3} - \frac{y ^{5}}{5})^{2} (\frac{2 x ^{4}}{3} + \frac{y ^{5}}{5})^{2}

s im pl i f y (\frac{3 d e ^{- 1}}{12 n e ^{2} f})^{- 3}

s im pl i f y e^{- 0.65} \cdot 0.6 5^{0} \cdot \frac{1}{0 !}

s im pl i f y (e^{y} + 1)^{2} e^{- y} d x

s im pl i f y (5 x) (4 x^{3})

s im pl i f y e^{- \frac{9}{8}}