Superscript in Math: Definition & Example

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

The superscript in math is used quite often. Learn how to easily spot a superscript when you are looking at math problems. Also discover the most popular use of the math superscript as well as another way of using it. Find out how to differentiate between the two.

What is a Superscript?

A superscript is the little number that is sometimes placed up and to the right of other numbers. The context of its use determines what the superscript's meaning is. Here are some examples of superscripts as used in math.

Here are some examples of the superscript in use.
superscript examples

See how all of these superscripts are written to the top right of their respective numbers? The superscript is applied to whatever number or variable is written to the bottom left of it. So, in the first example, the 7 is applied to the 5. In the second example, the 3 is applied to the f.

The Main Use of the Superscript

The first example, 5^7, demonstrates the most common use of the superscript. If you haven't already guessed it, it is the exponent or power use. The 7 in the example means that you multiply the 5 seven times. As an exponent or power, the superscript tells you how many times you are to multiply the number or variable it is next to. Here are some examples of how it works.

This is the superscript in use as an exponent or power.
superscript power examples

In the case of variables, even though the superscript tells you to multiply it so many times, you still write it with the superscript. But with numbers, you multiply it out. The first one tells you to multiply the 3 four times, with your answer being 81. The second one tells you to multiply the x three times, but since it is a variable, you still write it with the exponent.

The Secondary Use of the Superscript

The other use of the superscript is when it tells you which derivative is required.

The superscript in use as a derivative
superscript derivative

The above example tells you that the third derivative is asked for. Here are some more examples of this way of using the superscript.

The superscript in use as a derivative
superscript derivative examples

Each tells you how many derivatives to take of each function. The first tells you to take the derivative of the g(t) function twice. The second tells you to take the derivative of f(t) five times. The last tells you to take the derivative of h(x) three times.

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