Question

1. \frac{3x \cdot 3y^{3}}{2x^{-2}y^{2}}

Explanation:

Step1: Simplify the coefficients and variables separately

First, handle the coefficients: \( 3\times3 = 9 \). Then, handle the \( x \)-terms: \( x\times x^{-2}=x^{1 + (-2)}=x^{-1}=\frac{1}{x} \). Next, handle the \( y \)-terms: \( y^{3}\div y^{2}=y^{3 - 2}=y \). And the coefficient of the denominator for \( x \)-terms: \( 2 \) remains. So combining these, we have \( \frac{9\times\frac{1}{x}\times y}{2} \).

Step2: Rewrite the expression

Simplify the expression to get \( \frac{9y}{2x} \).

Answer:

\( \frac{9y}{2x} \)