1. 1. Complete the table to explore patterns in the exponents when dividing powers of 10. Use the “expanded” column to show why the given expression is equal to the single power 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. Use the patterns you found in the table to rewrite as an equivalent expression with a single exponent, like .
3. It is predicted that by 2050, there will be people living on Earth. At that time, it is predicted there will be approximately trees. How many trees will there be for each person?

So far we have looked at powers of 10 with exponents greater than 0. Consider what would happen to our patterns if we included 0 as a possible exponent?

1. 1. Write  as a single power of 10. Explain or show your reasoning.

   2. What number could you multiply by to get this same answer?
       

2. 1. Write as a single power of 10. Explain or show your reasoning.

   2. What number could you divide by to get this same answer?
       
3. In order for the exponent rules we found to work even when the exponent is 0, what does the value of have to be?

Write as many expressions as you can that have the same value as . Focus on using exponents, multiplication, and division.