Negative Exponents

Hello. In this math educational post, I go over working with negative exponents.

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Topics

• Exponents Review
• Dealing With Negative Exponents
• Practice Problems
• Answers To Practice Problems

Exponents Review

An exponent can be viewed as a number counter of how many times a number is multiplied by itself. Instead of writing 2 x 2 x 2 x 2 x 2, we can write where the base 2 is the number being multiplied by itself. The exponent 5 represents how many times the two is used when multiplying by itself.

When it comes to fractional exponents it is kind of difficult to explain what it is. Having is actually taking the square root of 2. When it comes to , this is taking the fifth root of 7. Consider the case where the exponent does not have a numerator of one such as . With I do ten squared to obtain 100 and then take the third root of 100.

With a non-zero base and an exponent zero the number results in a 1. Examples include in which they equal one.

Dealing With Negative Exponents

Negative exponents operate differently than positive exponents. It is common math practice to convert negative exponent values into its equivalent value with positive exponents.

Given this turns into its reciprocal of 1 divided by x:

The more confusing variation of the above is dealing with which ends up being x.

Example One

Evaluate .

Solution

Example Two

Evaluate one tenth to the power of negative 2.

Example Three

Convert the following expression into positive exponents.

Solution

With this case, you can "flip" the fraction and remove the negative signs from the exponents.

Practice Problems

Evaluate the following into a single number.

Convert into positive exponents.

Answers To Practice Problems

1. 1/8

2. 1/9

3. 1/4

4. 49/4

Convert into positive exponents.