In the diagram, the medium rectangle is made up of 10 small squares. The large square is made up of 10 medium rectangles.

1. How could the large square be represented as a power of 10? Explain your reasoning.
2. If each small square represents , then what does the medium rectangle represent? The large square?
3. If each small square represents , then what does the medium rectangle represent? The large square?

1. 1. Complete the table to explore patterns in the exponents when multiplying powers of 10. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it.

      expression	expanded	single power of 10

   2. If you chose to skip one entry in the table, which entry did you skip? Why?
2. 1. Use the patterns you found in the table to rewrite  as an equivalent expression with a single exponent, like .
   2. Use your rule to write with a single exponent.  What does this tell you about the value of ?
3. The state of Georgia has roughly human residents. Each human has roughly bacteria cells in his or her digestive tract. How many bacteria cells are there in the digestive tracts of all the humans in Georgia?

1. 1. Complete the table to explore patterns in the exponents when raising a power of 10 to a power. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it.

      expression	expanded	single power of 10

   2. If you chose to skip one entry in the table, which entry did you skip? Why?
2. Use the patterns you found in the table to rewrite as an equivalent expression with a single exponent, like .
3. If you took the amount of oil consumed in 2 months in 2013 worldwide, you could make a cube of oil that measures meters on each side. How many cubic meters of oil is this? Do you think this would be enough to fill a pond, a lake, or an ocean?