How to Divide Exponents

Exponents are a way of expressing repeated multiplications. For example, 3 x 3 x 3 x 3 can be written as 3^4. The exponent is the number of times the value is multiplied. The number or variable that is multiplied is called the base. In our example, four is the exponent and three is the base. An exponent of two is often referred to as "squaring" a number, and an exponent of three is called "cubing" a number. You can simplify exponents by multiplying and dividing them, as long as the two exponential expressions have the same base.

Instructions

1. Check that your two exponents have the same bases. You cannot divide exponents with different bases.

2. Write your equation as a fraction with a numerator and a denominator. For example, if you are dividing 3^5 by 3^2, write the equation as 3^5 (the numerator) over 3^2 (the denominator).

3. Subtract the denominator's exponent from the numerator's exponent. The resulting number is the exponent of the dividend; its base is your original base. For example, 3^5 divided by 3^2 equals 3^3.

Tips & Warnings

• You can multiply exponents with identical bases by adding the exponents.

References

• West Texas A&M: Beginning Algebra--Exponents