Simplify the given expression. Write answers with positive exponents.

$$\frac{m^2 n^3}{a^2 c^{-3}} \cdot \frac{a^{-7} n^{-2}}{m^2 c^4}$$

A prospective buyer wants to know how much grain a specific silo can hold. The area of the floor of the silo is $(2 x+9)^2$. The height of the silo is $10 x+10$, where $x$ is measured in feet. Expand the square and multiply by the height to find the expression that shows how much grain the silo can hold.

Consider this scenario: Fred earns $\$ 40$ mowing lawns. He spends $\$ 10$ on mp3s, puts half of what is left in a savings account, and gets another $\$ 5$ for washing his neighbor's car.

How much money does Fred keep?

Simplify the given expression. Write answers with positive exponents.

$$\left(6^2-24\right)^2 \div\left(\frac{x}{y}\right)^{-5}$$

Factor the polynomial.

$$361 x^2-121$$

Consider this scenario:

A school is installing a flagpole in the central plaza. The plaza is a square with side length $100 \mathrm{~yd}$ as shown in the figure below. The flagpole will take up a square plot with area $x^2-6 x+9 \mathrm{~yd}^2$.

Find the length of the base of the flagpole by factoring.

Simplify the given expression. Write answers with positive exponents.

$$\left(\frac{3^2}{a^3}\right)^{-2}\left(\frac{a^4}{2^2}\right)^2$$

Consider this scenario:

Charlotte has appointed a chairperson to lead a city beautification project. The first act is to install statues and fountains in one of the city's parks. The park is a rectangle with an area of $98 x^2+105 x-27 \mathrm{~m}^2$. The length and width of the park are perfect factors of the area. Note $l \times w=98 x^2+105 x-27 \mathrm{~m}^2$

At the northwest corner of the park, the city is going to install a fountain. The area of the base of the fountain is $9 x^2-25 \mathrm{~m}^2$. Factor the area to find the lengths of the sides of the fountain.

Aaron wants to mulch his garden. His garden is $x^2+18 x+81 \mathrm{ft}^2$. One bag of mulch covers $x^2-81 \mathrm{ft}^2$. Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.

Consider this scenario: Fred earns $\$ 40$ mowing lawns. He spends $\$ 10$ on mp3s, puts half of what is left in a savings account, and gets another $\$ 5$ for washing his neighbor's car.

Write the expression that represents the number of dollars Fred keeps (and does not put in his savings account). Remember the order of operations.

A developer wants to purchase a plot of land to build a house. The area of the plot can be described by the following expression: $(4 x+1)(8 x-3)$ where $x$ is measured in meters. Multiply the binomials to find the area of the plot in standard form.

Factor the polynomial.

$$4 h^2-12 h k+9 k^2$$

Simplify each expression.

$$\frac{\sqrt{12 x}}{2+2 \sqrt{3}}$$

Factor the polynomial.

$$y^2-6 y+9$$