Complete the table.

A table with two rows. First row, value, 16, 4 blanks, fraction 1 over 2, three blanks. Second row, exponent form, 2 to the fourth power, 8 blanks. Above the top row, arrows point column to column right to left, labeled time 2. Below the bottom row, arrows point column to column, left to right, labeled times question mark.

1. As you move toward the left, each number is being multiplied by 2. What is the multiplier as you move toward the right?
2. Use the patterns you found in the table to write as a fraction.
3. Write as a power of 2 with a single exponent.
4. What is the value of ?
5. From the work you have done with negative exponents, how would you write as a fraction?
6. How would you write as a fraction?

Lin, Noah, Diego, and Elena each chose an expression to start with and then came up with a new list of expressions — some of which are equivalent to the original and some of which are not.

Choose 2 of the 4 lists to analyze. For each list of expressions you choose to analyze, decide which expressions are not equivalent to the original. Be prepared to explain your reasoning.

1. Lin’s original expression is and her list is:

2. Noah’s original expression is and his list is:

3. Diego’s original expression is and his list is:

4. Elena’s original expression is and her list is:

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