Question

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

Explanation:

Step1: Simplify denominator constants/variables

Multiply constants and combine $x$-terms:
$4x^{-4} \cdot 3x^2 = (4 \cdot 3)x^{-4+2} = 12x^{-2}$

Step2: Rewrite the original expression

Substitute simplified denominator:
$\frac{2x^{-1}y^{-1}}{12x^{-2}}$

Step3: Simplify constants and $x$-terms

Divide constants, subtract $x$-exponents:
$\frac{2}{12}x^{-1-(-2)}y^{-1} = \frac{1}{6}x^{1}y^{-1}$

Step4: Rewrite positive exponents only

Convert negative exponent to reciprocal:
$\frac{x}{6y}$

Answer:

$\frac{x}{6y}$