Question

$\frac{(4x^{3}y^{2})(3x^{6}y^{3})}{24x^{11}y^{-2}}$

Explanation:

Step1: Multiply the coefficients and add exponents of like - bases in the numerator

Multiply 4 and 3, and add exponents of $x$ and $y$.
$(4x^{3}y^{2})(3x^{6}y^{3})=(4\times3)x^{3 + 6}y^{2+3}=12x^{9}y^{5}$

Step2: Simplify the fraction

Divide the numerator by the denominator.
$\frac{12x^{9}y^{5}}{24x^{11}y^{-2}}=\frac{12}{24}x^{9 - 11}y^{5-(-2)}$

Step3: Calculate the coefficient and simplify exponents

$\frac{12}{24}=\frac{1}{2}$, $x^{9 - 11}=x^{-2}$, $y^{5-(-2)}=y^{7}$
So the result is $\frac{1}{2}x^{-2}y^{7}=\frac{y^{7}}{2x^{2}}$

Answer:

$\frac{y^{7}}{2x^{2}}$