How to Simplify Rational Exponents

What is a Rational Exponent?A rational exponent is a rational number (or any number that can be represented as a fraction) that acts as an exponent. An exponent, or power, is a number to which another number is raised. You need to simply a rational exponent in order to simply your calculations. Here are some steps to get you started:

Things You'll Need

• Pencil, paper
• Calculator
• Internet Access

Instructions

to Simply Rational Exponents

1. Recognize your need. You need to establish where you need to make simplifications in the first place. How you do this depends on where your calculations are most difficult. Experts say you can determined this by categorizing the complexity of each operation.

2. Calculations need to have the same base. The two most common laws dictating how rational exponents are simplified only will work if your quantities are of the same base. For example, if you are trying to simplify 8^2 times 16^2 without making the bases the same, your numbers will get too large too fast. This can be very frustrating, especially if time is of the essence.

3. Rewrite your quantity. If you are multiplying or dividing two quantities of the same base “a,” but different exponents m and n, you may rewrite the quantity as base a raised to the sum (if multiplying) or difference (if dividing) of the exponents.

4. Reformat your exponential quantity that is raised to a power. If you have a quantity already raised to the m power, and if you need to raise it to the nth power, reformat it as the quantity raised to the product of the two exponents m and n.

5. Simply your negative exponents. If you have a quantity a raised to the negative nth power, you can rewrite it as the reciprocal of a to the nth.

Tips & Warnings

• Add exponents when multiplying.

• Keep your exponents assigned.

• Do not confuse multiplication of exponents with the addition process involving exponents.

Resources

• Algebra II: Rational Exponents