To simplify the expression \(\frac{-24x^4y^3}{8x^6y^2}\), we can start by reducing the coefficients and the variables separately.
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Coefficients: \(-24\) and \(8\) can be simplified: \[ \frac{-24}{8} = -3 \]
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Variables: For \(x\): \[ \frac{x^4}{x^6} = x^{4-6} = x^{-2} \] For \(y\): \[ \frac{y^3}{y^2} = y^{3-2} = y^1 = y \]
Now, putting it all together: \[ \frac{-24x^4y^3}{8x^6y^2} = -3 \cdot x^{-2} \cdot y \]
Since \(x^{-2}\) can be rewritten as \(\frac{1}{x^2}\), the final simplified expression is: \[ -\frac{3y}{x^2} \]
Thus, the simplified form of the original fraction is: \[ -\frac{3y}{x^2} \]