How to Solve Zero and Negative Exponents

How to Solve Zero and Negative Exponents

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

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

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