Question

complete the table.

problem: 3^-2, 2^-3, 10^-1, x^-2, x^-3, x^-4, x^-13, x^-1
value: 1/9, 1/8, 1/10, ___, ___, ___, ___, ___

Answer 1

To complete the table, we'll find the values of \( x^{-2} \), \( x^{-3} \), \( x^{-4} \), \( x^{-13} \), and \( x^{-1} \).

Recall that \( x^{-n} = \frac{1}{x^n} \).

### Given Problems and Their Values:
- \( 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \)
- \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \)
- \( 10^{-1} = \frac{1}{10^1} = \frac{1}{10} \)

### For \( x \):
The values of \( x^{-n} \) can be expressed in terms of \( \frac{1}{x^n} \). Let's summarize the computations:

1. **\( x^{-2} \)**:
\[
x^{-2} = \frac{1}{x^2}
\]

2. **\( x^{-3} \)**:
\[
x^{-3} = \frac{1}{x^3}
\]

3. **\( x^{-4} \)**:
\[
x^{-4} = \frac{1}{x^4}
\]

4. **\( x^{-13} \)**:
\[
x^{-13} = \frac{1}{x^{13}}
\]

5. **\( x^{-1} \)**:
\[
x^{-1} = \frac{1}{x}
\]

### Completing the Table:
Now, we can denote the values for the columns:

- \( x^{-2} = \frac{1}{x^2} \)
- \( x^{-3} = \frac{1}{x^3} \)
- \( x^{-4} = \frac{1}{x^4} \)
- \( x^{-13} = \frac{1}{x^{13}} \)
- \( x^{-1} = \frac{1}{x} \)

Since we don’t have specific values for \( x \), we cannot assign numerical values for these expressions without more information about \( x \).

Thus, the completed table looks like this:

| Problem | Value |
|----------|----------------|
| \( 3^{-2} \) | \( \frac{1}{9} \) |
| \( 2^{-3} \) | \( \frac{1}{8} \) |
| \( 10^{-1} \) | \( \frac{1}{10} \) |
| \( x^{-2} \) | \( \frac{1}{x^2} \) |
| \( x^{-3} \) | \( \frac{1}{x^3} \) |
| \( x^{-4} \) | \( \frac{1}{x^4} \) |
| \( x^{-13} \) | \( \frac{1}{x^{13}} \)|
| \( x^{-1} \) | \( \frac{1}{x} \) |

If you need specific numerical values, you would need to provide a value for \( x \).