What is (2/3 x^4-1/5 y^5)^2(2/3 x^4+1/5 y^5)^2 ?

The solution to (2/3 x^4-1/5 y^5)^2(2/3 x^4+1/5 y^5)^2 is ((2x^4)/3-(y^5)/5)^2((2x^4)/3+(y^5)/5)^2

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

simplify

(\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}

Solution steps

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

Apply exponent rule:

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

assuming

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}

Simplify

(\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}

Apply exponent rule:

(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}

(\frac{3 d e ^{- 1}}{12 n e ^{2} f})^{- 3}

e^{- 0.65} \cdot 0.6 5^{0} \cdot \frac{1}{0 !}

(2.3 x 1 0^{1}) (7 x 1 0^{6})

(e^{y} + 1)^{2} e^{- y} d x

(5 x) (4 x^{3})

What is (2/3 x^4-1/5 y^5)^2(2/3 x^4+1/5 y^5)^2 ?
The solution to (2/3 x^4-1/5 y^5)^2(2/3 x^4+1/5 y^5)^2 is ((2x^4)/3-(y^5)/5)^2((2x^4)/3+(y^5)/5)^2