To find the quotient of \( \frac{54x^2}{-9x^2} \), you can simplify the expression as follows:
- Divide the coefficients: \( \frac{54}{-9} = -6 \).
- Divide the variables: \( \frac{x^2}{x^2} = 1 \) (as long as \( x \neq 0 \)).
Combining these results gives:
\[ \frac{54x^2}{-9x^2} = -6 \cdot 1 = -6 \]
So, the quotient is \( -6 \).