How to Solve Zero and Negative Exponents

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

Related Topics

• How to Solve Powers of Products and Quotients
• How to Multiply Exponents
• How to Divide Exponents
• How to Solve Negative Exponents and Negative Bases
• How to Solve Scientific Notation

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. \(\color{blue}{x^{0}= {1} }\)

Zero and Negative Exponents – Example 1:

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

Solution:

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

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

Zero and Negative Exponents – Example 2:

Evaluate. \(\color{blue}{3^{–2}}\)

Solution:

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

Zero and Negative Exponents – Example 3:

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

Solution:

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

Zero and Negative Exponents – 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 for Solving Zero and Negative Exponents

Evaluate the following expressions.

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

Download Zero and Negative Exponents Worksheet

1. \(\color{blue}{\frac{1}{8}} \\\ \)
2. \(\color{blue}{ \frac{1}{343} } \\\ \)
3. \(\color{blue}{ \frac{1}{36} } \\\ \)
4. \(\color{blue}{ \frac{9}{4} } \\\ \)
5. \(\color{blue}{125}\)
6. \(\color{blue}{256}\)