Simplify each expression. Assume all variables are nonzero.

$$4^0$$

Simplify by rationalizing each denominator.

$$\frac{3 \sqrt{27}}{2 \sqrt{6}}$$

Use the advertisement for the following exercise. Write an expression to represent each total cost and then simplify it.

$$\begin{array}{|c|} \hline \begin{array}{} \text{ART SUPPLY SALE} \end{array}\\ \hline \begin{array}{c|c} \text{Colored Pencils} & \text{Sketch Books}\\ ^\$8.88 & ^\$9.96 &&\\ \hline \text{Acrylic Paints}& \text{Paint Brushes}\\ ^\$11.99 & ^\$14.99 &&\\ \end{array}\\ \hline \end{array}$$

cost of $3$ sketch books at a $10 \%$ discotut and $5$ acrylic paints at a $25 \%$ discount

For each equation find the value of $y$ when $x=-3,-2,0,2$, and $3$.

$$y=-2 x^2+5 x-7$$

Simplify each expression.

$$-4 a+2(12-4 a)$$

Simplify each expression. Assume all variables are nonzero.

$$\left(-x^4 y^2\right)^5$$

Simplify each expression. Assume all variables are nonzero.

$$\frac{-24 x^4 y^{-6}}{14 x^{-3} y^3}$$

While Neil Armstrong and Burz Aldrin walked on the Moon, the Apollo $11$ command module completed $1$ orbit every $119$ minutes.

Estimate the number of orbits the Apollo $11$ module would make in $1$ week if it continued at the same rate.

This problem will prepare you for the Multi-Step Test Prep on the mentioned page.

What is the range of this relation?

This problem will prepare you for the Multi-Step Test Prep on the mentioned page.

What is the domain of this relation?

While Neil Armstrong and Burz Aldrin walked on the Moon, the Apollo $11$ command module completed $1$ orbit every $119$ minutes.

The Apollo $11$ module made $30$ orbits. For how many hours did it orbit the Moon?

This problem will prepare you for the Multi-Step Test Prep on the mentioned page.

Does this relation represent a function? Why or why not?

While Neil Armstrong and Burz Aldrin walked on the Moon, the Apollo $11$ command module completed $1$ orbit every $119$ minutes.

Modify your expression from part a so that it represents the time in hours needed to complete $n$ orbits.

This problem will prepare you for the Multi-Step Test Prep on the mentioned page.

The relation $(0,20),(-20,0),(0,-20)$, and $(20,0)$ can be plotted to produce the vertices of a shape very common in Native American art. What shape is this?