# How to Solve Negative Exponents and Negative Bases? (+FREE Worksheet!)

Learn how to solve math problems containing negative exponents and negative bases.

## 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 $$(–5)^{ \ -2}=+\frac{1}{5^2}$$

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### 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: $$\color{blue}{(\frac{x^a}{x^b})^{-n} = (\frac{x^b}{x^a})^{n}} → {(\frac{3a}{2c})^{ \ -2} = (\frac{2c}{3a})^{2}= \frac{(2c)^2}{(3a)^2} = \frac{2^2 c^2}{3^2a^2}= \frac{4 c^2}{9a^2} }$$

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$14.99 Satisfied 92 Students ### 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. 1. $$\color{blue}{\frac{4ab^{-2}}{-3c^{-2}} } \\\$$ 2. $$\color{blue}{– 12x^2y^{-3} } \\\$$ 3. $$\color{blue}{(– \frac{1}{3})^{–2}} \\\$$ 4. $$\color{blue}{(– \frac{3}{4})^{–2}} \\\$$ 5. $$\color{blue}{(\frac{5x}{4y})^{–2}} \\\$$ 6. $$\color{blue}{(– \frac{5x}{3yz})^{–3}} \\\$$ ### Download Negative Exponents and Negative Bases Worksheet 1. $$\color{blue}{– \frac{4ac^2}{3b^2} } \\\$$ 2. $$\color{blue}{– \frac{12x^2}{y^3 }} \\\$$ 3. $$\color{blue}{9} \\\$$ 4. $$\color{blue}{\frac{16}{9}} \\\$$ 5. $$\color{blue}{\frac{16y^2}{25x^2 }} \\\$$ 6. $$\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 ### 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. X 45% OFF Limited time only! Save Over 45% SAVE$40

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