What is (x^2y^3+(x^2(x+y))/(x-y)+y^5)^6 ?

The solution to (x^2y^3+(x^2(x+y))/(x-y)+y^5)^6 is ((x^3y^3-x^2y^4+x^3+x^2y+xy^5-y^6)^6)/((x-y)^6)

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simplify (x^2y^3+(x^2(x+y))/(x-y)+y^5)^6

simplify

(x^{2} y^{3} + \frac{x ^{2} ( x + y )}{x - y} + y^{5})^{6}

\frac{( x ^{3} y ^{3} - x ^{2} y ^{4} + x ^{3} + x ^{2} y + x y ^{5} - y ^{6} ) ^{6}}{( x - y ) ^{6}}

Solution steps

(x^{2} y^{3} + \frac{x ^{2} ( x + y )}{x - y} + y^{5})^{6}

Join

x^{2} y^{3} + \frac{x ^{2} ( x + y )}{x - y} + y^{5} : \frac{x ^{3} y ^{3} - x ^{2} y ^{4} + x ^{3} + x ^{2} y + x y ^{5} - y ^{6}}{x - y}

= (\frac{x ^{3} y ^{3} - x ^{2} y ^{4} + x ^{3} + x ^{2} y + x y ^{5} - y ^{6}}{x - y})^{6}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( x ^{3} y ^{3} - x ^{2} y ^{4} + x ^{3} + x ^{2} y + x y ^{5} - y ^{6} ) ^{6}}{( x - y ) ^{6}}

\frac{4 m - 7}{2} = 18

6 t^{2} - 102 t

- x^{2} + 5 x + 24

- 6 - 2 s = - 6

(\frac{1 + 5}{2})^{2}

What is (x^2y^3+(x^2(x+y))/(x-y)+y^5)^6 ?
The solution to (x^2y^3+(x^2(x+y))/(x-y)+y^5)^6 is ((x^3y^3-x^2y^4+x^3+x^2y+xy^5-y^6)^6)/((x-y)^6)