What is the answer to solvefor y,3x^2y^4=5x^3y^{-3}z^2 ?

The answer to solvefor y,3x^2y^4=5x^3y^{-3}z^2 is y=\sqrt[7]{(5xz^2)/3};\quad x\ne 0

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solvefor y,3x^2y^4=5x^3y^{-3}z^2

solve for

y, 3 x^{2} y^{4} = 5 x^{3} y^{- 3} z^{2}

Solution steps

3 x^{2} y^{4} = 5 x^{3} y^{- 3} z^{2}

Refine

3 x^{2} y^{4} = \frac{5 x ^{3} z ^{2}}{y ^{3}}

Multiply both sides by

y^{3}

3 y^{7} x^{2} = 5 x^{3} z^{2}

Solve

\frac{( 1 + x ^{4} + x ^{8} )}{x ^{4}} = 4

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

\frac{3 x - 2}{x} = \frac{59 x ^{2} - 4}{x ^{2}}

(\frac{x + 1}{x})^{2} - 2 (\frac{x - 1}{x + 4}) - 11 = 0

\frac{21}{2 \cdot x} = \frac{331}{3}

What is the answer to solvefor y,3x^2y^4=5x^3y^{-3}z^2 ?
The answer to solvefor y,3x^2y^4=5x^3y^{-3}z^2 is y=\sqrt[7]{(5xz^2)/3};\quad x\ne 0