### Home > CCA > Chapter 7 > Lesson 7.2.2 > Problem7-97

7-97.

Consider the pattern at right.

1. Continue the pattern to find $\frac { 1 } { 2 ^ { - 1 } } , \frac { 1 } { 2 ^ { - 2 } } , \frac { 1 } { 2 ^ { - 3 } }$, and $\frac { 1 } { 2 ^ { - 4 } }$.

$2, 4, 8, 16$

2. What is the value of $\frac { 1 } { 2 ^ { - n } }$?

$2^{n}$

3. Write a conjecture about how to rewrite $\frac { 1 } { a ^ { - n } }$ without a negative exponent.

Use the same reasoning as in part (b).

$\left. \begin{array} { l } { \frac { 1 } { 2 ^ { 3 } } = \frac { 1 } { 8 } } \\ { \frac { 1 } { 2 ^ { 2 } } = \frac { 1 } { 4 } } \\ { \frac { 1 } { 2 ^ { 1 } } = \frac { 1 } { 2 } } \\ { \frac { 1 } { 2 ^ { 0 } } = 1 } \end{array} \right.$