How to Solve Negative Exponents and Negative Bases? (+FREE Worksheet!)
Learn how to solve math problems containing negative exponents and negative bases.
Related Topics
- How to Solve Powers of Products and Quotients
- How to Multiply Exponents
- How to Divide Exponents
- How to Solve Zero and Negative Exponents
- How to Solve Scientific Notation
Step by step guide to solve negative exponents and negative bases problems
- Make the power positive. A negative exponent is the reciprocal of that number with a positive exponent.
- The parenthesis is important! \(-5^{ \ -2}\) is not the same as \((– 5)^{ \ -2}\)
\(– 5^{ \ -2}= -\frac{1}{5^2} \) and \((–5)^{ \ -2}=+\frac{1}{5^2}\)
The Absolute Best Books to Ace Pre-Algebra to Algebra II
Negative Exponents and Negative Bases – Example 1:
Simplify. \((\frac{5a}{6c})^{ \ -2}=\)
Solution:
Use Exponent’s rules: \(\color{blue}{(\frac{x^a}{x^b})^{-n} = (\frac{x^b}{x^a})^{n}} → {(\frac{5a}{6c})^{ \ -2} = (\frac{6c}{5a})^{2}= \frac{(6c)^2}{(5a)^2} = \frac{6^2 c^2}{5^2a^2}= \frac{36 c^2}{25a^2} }\)
Negative Exponents and Negative Bases – Example 2:
Simplify. \((\frac{2x}{3yz})^{ \ -3}=\)
Solution:
Use Exponent’s rules: \(\color{blue}{(\frac{x^a}{x^b})^{-n} = (\frac{x^b}{x^a})^{n}} → {(\frac{2x}{3yz})^{ \ -3} = (\frac{3yz}{2x})^{3}= \frac{(3yz)^3}{(2x)^3} = \frac{3^3 y^3z^3}{2^3x^3}= \frac{27 y^3z^3}{8x^3} }\)
Negative Exponents and Negative Bases – Example 3:
Simplify. \((\frac{3a}{2c})^{-2}=\)
Solution:
Use Exponent’s rules: \(\color{blue}{(\frac{x^a}{x^b})^{-n} = (\frac{x^b}{x^a})^{n}} → {(\frac{3a}{2c})^{ \ -2} = (\frac{2c}{3a})^{2}= \frac{(2c)^2}{(3a)^2} = \frac{2^2 c^2}{3^2a^2}= \frac{4 c^2}{9a^2} }\)
The Best Book to Help You Ace Pre-Algebra
Negative Exponents and Negative Bases – Example 4:
Simplify. \((-\frac{5x}{3yz})^{-3}=\)
Solution:
Use Exponent’s rules: \(\color{blue}{\frac{1}{x^b} =x^{-b}} →(-\frac{5x}{3yz})^{-3}= \frac{ 1}{(-\frac{5x}{3yz})^3} = \frac{ 1}{-\frac{5^3 x^3}{3^3 y^3 z^3} }\)
Now use fraction rule: \(\color{blue}{\frac{1}{(\frac{b}{c})}=\frac{c}{b }} → \frac{ 1}{-\frac{ 5^3 x^3 }{ 3^3 y^3 z^3 } } = -\frac{ 3^3 y^3 z^3 }{ 5^3 x^3 }\)
Then: \( -\frac{ 27 y^3 z^3}{125x^3}\)
Exercises for Solving Negative Exponents and Negative Bases
Simplify.
- \(\color{blue}{\frac{4ab^{-2}}{-3c^{-2}} } \\\ \)
- \(\color{blue}{– 12x^2y^{-3} } \\\ \)
- \(\color{blue}{(– \frac{1}{3})^{–2}} \\\ \)
- \(\color{blue}{(– \frac{3}{4})^{–2}} \\\ \)
- \(\color{blue}{(\frac{5x}{4y})^{–2}} \\\ \)
- \(\color{blue}{(– \frac{5x}{3yz})^{–3}} \\\ \)
Download Negative Exponents and Negative Bases Worksheet
- \(\color{blue}{– \frac{4ac^2}{3b^2} } \\\ \)
- \(\color{blue}{– \frac{12x^2}{y^3 }} \\\ \)
- \(\color{blue}{9} \\\ \)
- \(\color{blue}{\frac{16}{9}} \\\ \)
- \(\color{blue}{\frac{16y^2}{25x^2 }} \\\ \)
- \(\color{blue}{– \frac{27y^3 z^3}{125x^3 }} \\\ \)
The Greatest Books for Students to Ace the Algebra
Related to This Article
More math articles
- Full-Length GRE Math Practice Test
- Best Graphing Calculators for Precalculus
- How to Unravel Constant and Identity Functions
- Rules of Exponents
- How do Find Amplitude, Period, and Phase Shift?
- Decimals Unfolded: How to Switch Between Standard and Expanded Forms
- 8th Grade PSSA Math Worksheets: FREE & Printable
- The Ultimate ALEKS Math Course (+FREE Worksheets & Tests)
- 5 Tips for Surviving a Statistics Course
- Grid Magic: How to Complete Decimal Multiplication Sentences
What people say about "How to Solve Negative Exponents and Negative Bases? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.