Question

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 \(\frac{-24x^4y^3}{8x^6y^2}\), 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:
\[
\frac{-24x^4y^3}{8x^6y^2} = -3 \cdot x^{-2} \cdot y
\]

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:
\[
-\frac{3y}{x^2}
\]