Questions: 2s^3y^2 / 4s^2y^5 * s y^-3

Solution Steps

To simplify the given expression, we need to apply the rules of exponents. Specifically, we will divide the coefficients, subtract the exponents of like bases in the numerator and the denominator, and simplify any remaining terms.

We start with the expression: \[ \frac{2 s^{3} y^{2}}{4 s^{2} y^{5}} \cdot s \cdot y^{-3} \]

First, we simplify the coefficients: \[ \frac{2}{4} = \frac{1}{2} \]

Next, we simplify the variables. For \(s\): \[ \frac{s^{3}}{s^{2}} \cdot s = s^{3 - 2 + 1} = s^{2} \] For \(y\): \[ \frac{y^{2}}{y^{5}} \cdot y^{-3} = y^{2 - 5 - 3} = y^{-6} \]

Combining the simplified coefficients and variables, we have: \[ \frac{s^{2}}{2 y^{6}} \]

Final Answer