Zero and Negative Exponents

Zero and Negative Exponents

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.

  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. \(\color{blue}{256}\)

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