Start Fraction negative 24 x superscript 4 baseline y cubed over 8 x superscript 6 baseline y squared End Fraction

Answer 1

To simplify the expression $\frac{-24x^4{y}^3}{8x^6{y}^2}$, we can start by reducing the coefficients and the variables separately.

1. Coefficients: $-24$ and $8$ can be simplified: $$\frac{-24}{8}=-3$$

2. 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: $$\frac{-24x^4{y}^3}{8x^6{y}^2}=-3\cdot x^{-2}\cdot y$$

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: $$-\frac{3y}{x^2}$$