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.

Select all the expressions that are equivalent to \(10^{10}\)

An amoeba divides to form two amoebas after one hour. One hour later, each of the two amoebas divides to form two more. Every hour, each amoeba divides to form two more.

1. How many amoebas are there after 1 hour?
2. How many amoebas are there after 2 hours?
3. Write an expression for the number of amoebas after 6 hours.
4. Write an expression for the number of amoebas after 24 hours.
5. Why might exponential notation be preferable to answer these questions?

You have two numbers, \((x,y)\). If you triple the second number and subtract it from the first, the difference is 12.

1. Write an equation that describes the statement.
2. Is \((9,1)\) a solution to your equation? Explain how you know.
3. Find the second number if the first is 18.
4. Find the first number if the second number is \(\frac13\).