Question

Solve this power equation with rational exponents.

Answer 1

\[2y ^{-\frac{ 2 }{ 3 }}-5y ^{-\frac{ 1 }{ 3 }}-7=0 \]

Answer 2

well you are basically looking at a quadratic equation

\[2(y^{\frac{1}{3}})^2 - 5(y^{\frac{1}{3}}) - 7 = 0\]

so you can make a subsitution such as

\[u = y^{\frac{1}{3}} \] and the solve

or just factor the equation to

\[(2y^{\frac{1}{3}} - 7)(y^{\frac{1}{3}} + 1) = 0\]

so you need to solve

\[2y^{\frac{1}{3}} - 7 = 0\]

and

\[y^{\frac{1}{3}} + 1 = 0\]

hope it helps