Question

1. \\(\frac{3xy^{2} cdot 2x^{-3}}{2y^{4}}\\)

Explanation:

Step1: Multiply numerator constants

$3 \times 2 = 6$

Step2: Combine x terms via exponent rule

$x^1 \cdot x^{-3} = x^{1 + (-3)} = x^{-2}$

Step3: Simplify fraction constants

$\frac{6}{2} = 3$

Step4: Combine y terms via exponent rule

$\frac{y^2}{y^4} = y^{2 - 4} = y^{-2} = \frac{1}{y^2}$

Step5: Rewrite negative x exponent

$x^{-2} = \frac{1}{x^2}$

Step6: Combine all simplified terms

$3 \cdot \frac{1}{x^2} \cdot \frac{1}{y^2}$

Answer:

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