1. What is the volume of a cube with an edge length of

   1. 4 centimeters?

   2. \(\sqrt[3]{11}\) feet?

   3. \(s\) units?

2. What is the edge length of a cube with a volume of

   1. 1,000 cubic centimeters?

   2. 23 cubic inches?

   3. \(v\) cubic units?

Write an equivalent expression that doesn’t use a cube root symbol.

1. \(\sqrt[3]{1}\)
2. \(\sqrt[3]{216}\)
3. \(\sqrt[3]{8,000}\)
4. \(\sqrt[3]{\frac{1}{64}}\)
5. \(\sqrt[3]{\frac{27}{125}}\)
6. \(\sqrt[3]{0.027}\)
7. \(\sqrt[3]{0.000125}\)

Find the distance (in units) between each pair of points. If you get stuck, try plotting the points on graph paper.

1. \(X=(5,0)\) and \(Y=(\text-4,0)\)

2. \(K=(\text-21,\text-29)\) and \(L=(0,0)\)

Here is a 15-by-8 unit rectangle divided into triangles. Is the shaded triangle a right triangle? Explain or show your reasoning.

A rectangle with a point on the bottom side. Two line segments are drawn from the point to the top left vertex and from the point to the top right vertex of the rectangle creating 3 triangles. The left side of the rectangle is labeled 8. The segment from the bottom left corner of the rectangle to the point on the bottom side is labeled 9. The segment from the point on the bottom side to the bottom right corner is labeled 6. The middle triangle is shaded.

Express each of the following as a single power of 10:

1. 100

2. 100,000

3. 100,000,000

4. \(100 \boldcdot 10\)

5. \(1,000 \boldcdot 1,000\)