a square floor has a side length of 7x^5y^6 units. a square tile has a side length of x^2y units. how many…

Explanation:

Step1: Find area of floor

The area of a square floor with side - length $s_1 = 7x^{5}y^{6}$ is $A_1=s_1^{2}=(7x^{5}y^{6})^{2}$. Using the power - of - a - product rule $(ab)^n=a^n b^n$ and power - of - a - power rule $(a^m)^n=a^{mn}$, we get $A_1 = 49x^{10}y^{12}$.

Step2: Find area of tile

The area of a square tile with side - length $s_2=x^{2}y$ is $A_2=s_2^{2}=(x^{2}y)^{2}=x^{4}y^{2}$.

Step3: Calculate number of tiles

The number of tiles $n$ is the ratio of the area of the floor to the area of the tile, so $n=\frac{A_1}{A_2}=\frac{49x^{10}y^{12}}{x^{4}y^{2}}$. Using the quotient rule $\frac{a^m}{a^n}=a^{m - n}$, we have $n = 49x^{10-4}y^{12 - 2}=49x^{6}y^{10}$.

Answer:

$49x^{6}y^{10}$