Learn how to solve mathematical problems containing Zero and Negative Exponents using exponents formula.

## Step by step guide to solve zero and negative exponents problems

- A negative exponent simply means that the base is on the wrong side of the fraction line,so you need to flip the base to the other side. For instance, “\(x^{ \ -2}\)” (pronounced as “ecks to the minus two”) just means “\(x^2\)” but underneath, as in \(\frac{1}{x^2}\).
- Any number (except zero) to the power of zero is 1. \(\color{blue}{x^{0}= {1} }\)

### Example 1:

Evaluate. \((\frac{2x}{3}) ^{ \ 0} =\)

**Solution:**

Use Exponent’s rules: \(\color{blue}{x^{0}= {1} }\)

Then: \((\frac{2x}{3}) ^{ \ 0} = { \ 1} \)

### Example 2:

Evaluate. \(\color{blue}{3^{–2}}\)

**Solution:**

Use Exponent’s rules: \(\color{blue}{x^{-b}= \frac{1}{x^b} } → 3^{-2}= \frac{1}{3^2}= \frac{1}{9} \)

### Example 3:

Simplify. \((\frac{3}{2})^{-2}=\)

**Solution:**

Use Exponent’s rules: \(\color{blue}{(\frac{x^a}{x^b})^{-n} = (\frac{x^b}{x^a})^{n}} → {(\frac{3}{2})^{ \ -2} = (\frac{2}{3})^{2}= \frac{(2)^2}{(3)^2} = \frac{4}{9} }\)

### Example 4:

Evaluate. \((\frac{5}{6})^{-3}=\)

**Solution:**

Use Exponent’s rules: \(\color{blue}{(\frac{x^a}{x^b})^{-n} = (\frac{x^b}{x^a})^{n}} → {(\frac{5}{6})^{ \ -3} = (\frac{6}{5})^{3}= \frac{(6)^3}{(5)^3} = \frac{216}{125} }\)

## Exercises

### Evaluate the following expressions.

- \(\color{blue}{8^{–1}}\)
- \(\color{blue}{7^{–3}}\)
- \(\color{blue}{6^{–2}}\)
- \(\color{blue}{(\frac{2}{3})^{–2}} \\\ \)
- \(\color{blue}{(\frac{1}{5})^{– 3}} \\\ \)
- \(\color{blue}{(\frac{1}{2})^{–8}}\)

### Download Zero and Negative Exponents Worksheet

- \(\color{blue}{\frac{1}{8}} \\\ \)
- \(\color{blue}{ \frac{1}{343} } \\\ \)
- \(\color{blue}{ \frac{1}{36} } \\\ \)
- \(\color{blue}{ \frac{9}{4} } \\\ \)
- \(\color{blue}{125}\)
- \(\color{blue}{256}\)