Questions: 3y^3 / 5 * (x^7 / 2y^8)^2

Solution Steps

We start with the expression \( \frac{3 y^{3}}{5} \cdot \left( \frac{x^{7}}{2 y^{8}} \right)^{2} \).

First, we simplify the second expression \( \left( \frac{x^{7}}{2 y^{8}} \right)^{2} \): \[ \left( \frac{x^{7}}{2 y^{8}} \right)^{2} = \frac{x^{14}}{4 y^{16}} \]

Next, we multiply the two expressions: \[ \frac{3 y^{3}}{5} \cdot \frac{x^{14}}{4 y^{16}} = \frac{3 y^{3} \cdot x^{14}}{5 \cdot 4 y^{16}} = \frac{3 x^{14} y^{3}}{20 y^{16}} \]

Now, we simplify the resulting expression: \[ \frac{3 x^{14} y^{3}}{20 y^{16}} = \frac{3 x^{14}}{20 y^{13}} \]

The final simplified expression is: \[ \frac{3 x^{14}}{20 y^{13}} \]

Final Answer