What is (((2y^2)^2))/((2x^{-2)*y^{-1}-2x^4*y^3)} ?

The solution to (((2y^2)^2))/((2x^{-2)*y^{-1}-2x^4*y^3)} is (2y^5x^2)/(1-y^4x^6)

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simplify (((2y^2)^2))/((2x^{-2)y^{-1}-2x^4y^3)}

simplify

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

\frac{2 y ^{5} x ^{2}}{1 - y ^{4} x ^{6}}

Solution steps

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

2 x^{- 2} y^{- 1} = \frac{2}{y x ^{2}}

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

(2 y^{2})^{2} = 2^{2} y^{4}

= \frac{2 ^{2} y ^{4}}{\frac{2}{y x ^{2}} - 2 y ^{3} x ^{4}}

Join

\frac{2}{x ^{2} y} - 2 x^{4} y^{3} : \frac{2 - 2 y ^{4} x ^{6}}{y x ^{2}}

= \frac{2 ^{2} y ^{4}}{\frac{2 - 2 y ^{4} x ^{6}}{y x ^{2}}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{2 ^{2} y ^{4} x ^{2} y}{2 - 2 x ^{6} y ^{4}}

Factor

2 - 2 x^{6} y^{4} : 2 (1 - x^{6} y^{4})

= \frac{2 ^{2} y ^{4} x ^{2} y}{2 ( 1 - x ^{6} y ^{4} )}

Cancel the common factor:

2

= \frac{2 y ^{4} y x ^{2}}{1 - y ^{4} x ^{6}}

2 y^{4} y x^{2} = 2 y^{5} x^{2}

= \frac{2 y ^{5} x ^{2}}{1 - y ^{4} x ^{6}}

\frac{x ^{2} + 11 x + 26}{- ( x + 3 )}

2 x^{2} + 13 x y - 24 y^{2}

a^{2} m^{3}

(w^{7})^{- 2}

2 x (4 y + x)

What is (((2y^2)^2))/((2x^{-2)*y^{-1}-2x^4*y^3)} ?
The solution to (((2y^2)^2))/((2x^{-2)*y^{-1}-2x^4*y^3)} is (2y^5x^2)/(1-y^4x^6)