Question

1. $\frac{15x^{2}ycdot - 6x^{7}y}{(3xy)^{2}}$

Explanation:

Step1: Expand the denominator

First, expand $(3xy)^2$ using the power - of - a - product rule $(ab)^n=a^n b^n$. So, $(3xy)^2 = 3^2x^2y^2=9x^2y^2$.

Step2: Multiply the numerator

Multiply $15x^{2}y$ and $- 6x^{7}y$ in the numerator. Using the rule $a^m\times a^n=a^{m + n}$ and $ab\times cd=ac\times bd$, we get $15\times(-6)x^{2 + 7}y^{1+1}=-90x^{9}y^{2}$.

Step3: Simplify the fraction

Now, simplify $\frac{-90x^{9}y^{2}}{9x^{2}y^{2}}$. Using the rule $\frac{a^m}{a^n}=a^{m - n}$ and $\frac{ac}{bc}=\frac{a}{b}(b
eq0)$, we have $\frac{-90}{9}x^{9 - 2}y^{2-2}=- 10x^{7}$.

Answer:

$-10x^{7}$