How do exponents work with fractions

Fractional exponents play a role in computing the orbital period of a planet. Image by Comfreak. In their simplest form, exponents stand for repeated multiplication. The smallish number the exponent , or power located to the upper right of main number the base tells how many times to use the base as a factor. You can even have a power of 1. For example, you may already know that the zero exponent on any base results in the number 1 with one exception: 0 0 is undefined.

So, reading the above equation backwards, we have discovered the rule for negative exponents! The more negative the exponent, the smaller the value. This is especially important in the sciences when talking about orders of magnitude how big or small things are.

For instance,. Except in one case: If the bases are different but the exponents are the same , then you can combine them. And it works for any common power of two different bases:. What about dividing?

Remember that dividing is just multiplying by 1-over-something. So all the laws of division are really just laws of multiplication. Well, there are several ways to work it out.

However you slice it, you come to the same answer: for division with like bases you subtract exponents , just as for multiplication of like bases you add exponents:. As that example illustrates, you can combine like exponents even when the bases are different:. Use the rule you already know for dividing:. Write each of these as a single positive power.

What do you do with an expression like x 5 4? How many factors of x are there? Exponents show the number of times a number is replicated in multiplication. Here, exponent 2 is a whole number. Fractional exponents are ways to represent powers and roots together.

In any general exponential expression of the form a b , a is the base and b is the exponent. When b is given in the fractional form, it is known as a fractional exponent. There are certain rules to be followed that help us to multiply or divide numbers with fractional exponents easily.

Many people are familiar with whole-number exponents, but when it comes to fractional exponents, they end up doing mistakes that can be avoided if we follow these rules of fractional exponents. These rules are very helpful while simplifying fractional exponents. Let us now learn how to simplify fractional exponents. Simplifying fractional exponents can be understood in two ways which are multiplication and division. It involves reducing the expression or the exponent to a reduced form that is easy to understand.

Let us understand the simplification of fractional exponents with the help of some examples. In this example, both the base and the exponent are in fractional form. As with multiplication, you may also end up with fractional exponents that have a number other than one in the numerator, but you deal with these in the same way. If the bases on the terms are different, there is no easy way to multiply or divide exponents.

In these cases, simply calculate the value of the individual terms and then perform the required operation. The only exception is if the exponent is the same, in which case you can multiply or divide them as follows:. Lee Johnson is a freelance writer and science enthusiast, with a passion for distilling complex concepts into simple, digestible language.

He's written about science for several websites including eHow UK and WiseGeek, mainly covering physics and astronomy. He was also a science blogger for Elements Behavioral Health's blog network for five years.