Write each expression as a single power of 10:

1. \(10^3 \boldcdot 10^9\)

2. \(10 \boldcdot 10^4\)

3. \(10^{10} \boldcdot 10^7\)

4. \(10^3 \boldcdot 10^3\)

5. \(10^5 \boldcdot 10^{12}\)

6. \(10^6 \boldcdot 10^6 \boldcdot 10^6\)

A large rectangular swimming pool is 1,000 feet long, 100 feet wide, and 10 feet deep. The pool is filled to the top with water. Express your answers both as a single power of 10 and as a number in standard form.

1. What is the area of the surface of the water in the pool?
2. How much water does the pool hold?

Write each expression with a single exponent:

1. \((10^7)^2\)

2. \((10^9)^3\)

3. \((10^6)^3\)

4. \((10^2)^3\)

5. \((10^3)^2\)

6. \((10^5)^7\)

You have 1,000,000 number cubes, each measuring 1 inch on a side.

1. If you stacked the cubes on top of one another to make an enormous tower, how high would they reach? Explain your reasoning.
2. If you arranged the cubes on the floor to make a square, would the square fit in your classroom? What would its dimensions be? Explain your reasoning.
3. If you layered the cubes to make one big cube, what would be the dimensions of the big cube? Explain your reasoning.