## Virtual Help

• Chat with library staff now
The Learning Portal - College Libraries Ontario

# 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 - RTF

## Examples

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.

### Activity

Try this activity to test your skills. If you have trouble, check out the information in the module for help.