Question

A few examples of expressions with negative exponents are given. 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 will calculate the values of the expressions with negative exponents and fill in the missing values.

Negative exponents represent the reciprocal of the positive exponent. For example, \( a^{-n} = \frac{1}{a^n} \).

Here's the completed table:

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

Now all examples with expressions and their corresponding values are filled in.