Addition & Subtraction of Rational Exponents

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  • 0:04 Rational Exponenets
  • 0:57 Rational Exponent Steps
  • 1:39 Rational Exponent Example
  • 3:06 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education

In this lesson, we'll discuss how to add and subtract rational exponents, which are exponents that contain fractions rather than full integers. We'll take a closer look at how these exponents work and then look at a few examples.

Rational Exponents

When studying math, it's common to look for patterns when solving problems. For example, the process for adding and subtracting fractions: we need to determine a common denominator; then we can add or subtract the numerators. Let's focus on learning the pattern to follow when adding and subtracting rational exponents.

First off, what is a rational exponent? Exponents are values that are written as a superscript on another value or variable. The exponents can be integers such as 2, 3, or 4; or they can be fractions such as ½, 2/3 or 4/5. These fractions are rational exponents. Put simply, a rational exponent is an exponent that is a fraction.

A good example of a rational exponent is x1/2. Before we get into what x1/2 means, let's look at a general case for a rational exponent, which is xa/b.

Rational Exponent Steps

When you see a rational exponent, you first write the variable, x in this case, under the radical symbol, or the square root of x in this case. The next step is to put the denominator of the exponent in the crook part of the radical sign, or b in this case. The final step is to put the numerator of the exponent as an exponent on the variable, or a in this case.

Let's go back to our example of x1/2 and rewrite it in radical form. Remember, the 2 goes in the crook, and the 1 follows the x. Notice that if you just write the variable under the radical sign without a value in the crook of the radical, it's assumed to be the square root of the value inside the radical.

Rational Exponent Example

Now let's focus on adding and subtracting two terms with rational exponents that contain the same base, root, and exponent. We'll start with this example:

101/4 + 5 (101/4)

Notice that the base (10) is the same in both values. The root is the same as well, and it is 4. The power is also the same, and it is 1. Let's rewrite this problem using the radical symbol:

4sqrt(10) + 5(4sqrt(10))

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