How to Divide Numbers With Exponents

Exponents are a shorthand version of the same number multiplied by itself a number of times. For example, instead of writing x*x*x*x*x*x, it is much faster and clearer to write x^6. In the expression x^6, x is the base number, and 6 is the exponent. To divide the exponents, you must have like bases. Once you have found the like bases, solving is a matter of organization rather than complicated mathematic reasoning.

Instructions

1. Find the like bases. The same base must occur in both the numerator and the denominator. For example, in the expression x^5/x^3, the base "x" appears in both the numerator and the denominator. As a result, you can simplify the expression.

2. Determine the exponent of the like base in the numerator. For example, in the problem x^5/x^3, 5 is the exponent in the numerator.

3. Determine the exponent of the like base in the denominator. For example, in the problem x^5/x^3, 3 is the exponent in the denominator.

4. Subtract the exponent in the numerator from the exponent in the denominator to find the resulting exponent. For example, 5'3=2, so x^5/x^3 is x^2.

Tips & Warnings

• If the exponent on the bottom is greater than the exponent on the top, such as in the expression y^5/y^9, you will get a negative exponent in the answer. You can either write the result as y^'4 or 1/y^4.

• If there are no like bases, you cannot simplify the expression. For example, if your expression is x^5/y^3, you cannot simplify the expression.

References

• Purple Math: Exponents: Basic Rules
• SOS Math: Exponential Rules