Find the value of mentally.

A table with three rows. Top row, using exponents, 10 cubed, 10 squared, 10 to the first power, blank, blank, blank, blank. Second row, as a decimal, 1000 point 0, blank, blank, 1 point 0, blank, 0 point 0 1, blank. Third row, as a fraction, blank, fraction 100 over 1, blank, fraction 1 over 1, blank, blank, fraction 1 over one thousand. Above the row, arrows point from column to column, right to left, each labeled times 10. Below the bottom row, arrows point from column to column, left to right, each labeled time question mark.

1. Complete the table to explore what negative exponents mean.
2. As you move toward the left, each number is being multiplied by 10. What is the multiplier as you move right?
3. How does a multiplier of 10 affect the exponent? How does it affect the value of the decimal and fraction?  
    
4. How does the other multiplier affect the exponent? How does it affect the value of the decimal and fraction?  
    
5. Use the patterns you found in the table to write as a fraction.
    
6. Use the patterns you found in the table to write as a decimal.
    
7. Write using a single exponent.
    
8. Use the patterns in the table to write as a fraction.

1. 1. Match each exponential expression with an equivalent multiplication expression:

      
      
   2. Write as a power of 10 with a single exponent. Be prepared to explain your reasoning.

2. 1. Match each exponential expression with an equivalent multiplication expression:

      
      
   2. Write as a power of 10 with a single exponent. Be prepared to explain your reasoning.

3. 1. Match each exponential expression with an equivalent multiplication expression:

      
      
   2. Write as a power of 10 with a single exponent. Be prepared to explain your reasoning.