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Math: Basic Tutorials : Exponent Rules
Exponent Rules
An exponent, also known as a power, indicates repeated multiplication of the same quantity. For example, we can write 2∙2∙2∙2 in exponential notation as 2 to the power of 4, where 2 is the base and 4 is the exponent (or power). We can read this as 2 to the fourth power or 2 to the power of 4. This module will review the properties of exponents that can be used to simplify expressions containing exponents.
Exponent Rules
Exponent Rules Video transcript - RTFExamples
Click on the titles below to view each example.
Simplify the expression: open parenthesis p to the power of 9 q to the power of negative two close parenthesis open parenthesis p to the power of negative six q squared close parenthesis.
Line 1. Use the product property and add the exponents of the same bases: p to the power of 6 plus negative 9 end superscript q to the power of negative 2 plus 2 end superscript.
Line 2. Simplify the exponents: p cubed q to the power of 0.
Line 3. Use the zero exponent property: p cubed times 1.
Line 4. Simplify to the final expression: p cubed.
Simplify the expression: Fraction: open parenthesis y squared close parenthesis cubed open parenthesis y squared close parenthesis to the power of 4 over open parenthesis y to the power of 5 close parenthesis to the power of 4 end fraction.
Line 1. Use the power property. Begin Fraction: Open parenthesis y to the 2 times 3 end superscript close parenthesis open parenthesis y to the 2 times 4 end superscript close parenthesis over y to the 5 times 4 end superscript end fraction.
Line 2. Multiply the exponents to simplify. Begin fraction: y to the 6 y to the 8 over y to the 20, end fraction.
Line 3. Use the product property in the numerator. Begin fraction: y to the 6 plus 8 end superscript over y to the 20, end fraction.
Line 4. Add the exponents to simplify. Begin fraction: y to the 14 over y to the 20, end fraction
Line 5. Use the quotient property. y to the 14 minus 20 end superscript.
Line 6. Subtract the exponents to simplify. y to the negative 6.
Line 7. Write negative exponents as positive for final answer. Begin fraction: 1 over y to the 6, end fraction.
Simplify the expression: Open parenthesis begin fraction 2x cubed over 3y end fraction close parenthesis to the power of 4.
Line 1. Raise the numerator and a denominator to the power of 4 using the quotient to a power property. Begin fraction: open parenthesis 2x cubed close parenthesis to the power of 4 over open parenthesis 3y close parenthesis to the power of 4, end fraction.
Line 2. Raise each factor to the power of 4 using the Product to a Power Property. Begin fraction: 2 to the power of 4 open parenthesis x cubed close parenthesis to the power of 4 over 3 to the power of 4 y to the power of 4, end fraction.
Line 3: Apply exponents and use the Power Property to simplify. Begin fraction: 16 x to the power of 12 over 81 y to the power of 4, end fraction.
Summary and Worksheet
- Summary: Exponent Rules - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Exponent Rules - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
Attribution
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window