Questions: Solve the following equation. If needed, submit your answer as a fraction reduced to lowest terms. y^(2/3) - 1/25 = 0

Solution Steps

To solve the given radical equation \( y^{\frac{2}{3}} - \frac{1}{25} = 0 \), we need to isolate \( y \). Here are the high-level steps:

1. Add \(\frac{1}{25}\) to both sides of the equation.
2. Raise both sides to the power of \(\frac{3}{2}\) to solve for \( y \).

Starting with the equation: \[ y^{\frac{2}{3}} - \frac{1}{25} = 0 \] we add \(\frac{1}{25}\) to both sides: \[ y^{\frac{2}{3}} = \frac{1}{25} \]

Next, we raise both sides to the power of \(\frac{3}{2}\) to solve for \(y\): \[ y = \left(\frac{1}{25}\right)^{\frac{3}{2}} \]

Calculating \(\left(\frac{1}{25}\right)^{\frac{3}{2}}\): \[ \left(\frac{1}{25}\right)^{\frac{3}{2}} = \frac{1^{3}}{25^{\frac{3}{2}}} = \frac{1}{\sqrt{25^3}} = \frac{1}{\sqrt{15625}} = \frac{1}{125} = 0.008 \]

Final Answer