How to Simplify Positive Exponents

Exponents are a way of shortening mathematical expressions where like terms are multiplied. Exponents have a power and a base. The base is the number being raised to a certain power. For example, in the expression four to the sixth power, four is the base and six is the exponent. When representing exponents on the computer, the caret (^) is often used in place of "raised to the power of." For example, three raised to the fifth power could also be written as 3^5. You can simplify positive exponents when they are raised to a further exponent, multiplied or divided.

Instructions

1. Simplify exponents that are raised to another power by multiplying the exponents. For example, x raised to the third power raised to the fourth power would simplify to x raised to the 12th power because three times four is 12.

2. Determine if there are any like bases of exponents being multiplied or divided. In order to simplify exponents, the bases must be the same. For example, you could simplify x^5 times x^3 but not t^5 times y^5.

3. Add the exponents of like bases being multiplied. For example, x^5 times x^3 would be x^8.

4. Subtract the exponents of like bases being divided. For example, y^8 divided by y^2 would be y^6.

Tips & Warnings

• You cannot simplify exponents when they are being added or subtracted even if they have like bases.

References

• PurpleMath.com: Exponents - Basic Rules
• SOSMath.com: Exponential Rules