Question

simplify the expression below

1. (\frac{6x^{-3}y^{-11}}{x^{-5}y^{-2}} =)

Explanation:

Step1: Separate coefficients and variables

$\frac{6x^{-3}y^{-11}}{x^{-5}y^{-2}} = 6 \cdot \frac{x^{-3}}{x^{-5}} \cdot \frac{y^{-11}}{y^{-2}}$

Step2: Simplify $x$-terms (subtract exponents)

$\frac{x^{-3}}{x^{-5}} = x^{-3 - (-5)} = x^{2}$

Step3: Simplify $y$-terms (subtract exponents)

$\frac{y^{-11}}{y^{-2}} = y^{-11 - (-2)} = y^{-9} = \frac{1}{y^{9}}$

Step4: Combine all simplified parts

$6 \cdot x^{2} \cdot \frac{1}{y^{9}}$

Answer:

$\frac{6x^{2}}{y^{9}}$