Quotient Rule for Exponents

The Quotient Rule of Exponent
The Quotient Rule of Exponents states that when you divide two powers that have the same base, you can subtract the exponent of the denominator from the exponent of the numerator. The base remains the same.

Example:
3⁶ / 3² = 3^{6 - 2} = 3⁴

How to Apply the Quotient Rule:

1. Check if the bases are the same: The quotient rule only applies when the numbers or variables being divided have the same base.
2. Subtract the exponents: If the bases are the same, keep the base and subtract the exponent in the denominator from the exponent in the numerator (m − n).

The following diagram shows the quotient rule for exponents. Scroll down the page for more examples and solutions for the exponential rules.

 

Rules of Exponents
Refer to the following for more Rules of Exponents:
Rules of Exponents

• Worksheets to Practice Exponent Rules

  Printable
  Product Rule
  Quotient Rule
  Power Rule
  Negative Exponents
  Fractional exponents
  Laws of Exponents
  

  Online
  Apply Law of Exponents (multiply)
  Apply Law of Exponents (mixed)
  

Quotient Rule of Exponents
How to divide numbers with exponents.

Simplify Exponential Expressions - Quotient Rule
This video provides several examples of how to simplify exponential expressions. The quotient rule is emphasized.

The Quotient Rule - Dividing with Exponents
Learn the quotient rule, which states that when dividing two powers that have the same base, subtract the exponents.

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.