When it comes to mathematical concepts, those tiny numeral superscripts called exponents can intimidate even the most earnest student. One thing that helps stop the anxiety is understanding the importance of exponents in everyday math applications.

#### TL;DR (Too Long; Didn't Read)

Exponents are supercript numerals that let you know how many times you should multiply a number by itself. Some real world applications include understanding scientific scales like the pH scale or the Richter scale, using scientific notation to write very large or very small numbers and taking measurements.

## What Are Exponents?

Quite simply, exponents tell you to multiply a number by itself using the superscript numeral to determine how many times you do this. For example, 10^{2} is the same as 10 x 10, or 100. 10^{5} is the same as 10 x 10 x 10 x 10 x 10, or 100,000.

## Scientific Scales

Any time that a scientific field uses a scale, like the pH scale or the Richter scale, you can bet you will find exponents. Both the pH scale and the Richter scale are logarithmic relationships with each whole number representing a ten-fold increase from the number before it.

For example, when chemists indicate a substance has a pH of 7, they know this represents 10^{7} while a substance with a pH of 8 represents 10^{8}. This means that the substance with the pH of 8 is 10 times more basic than the substance with the pH of 7.

Geophysicists also use a logarithmic scale. An earthquake that measures a 7 on the Richter scale clocks in at 10^{7} for seismic energy while an earthquake measuring an 8 represents 10^{8} for seismic energy. This means the second earthquake is 10 times more powerful than the first.

## Writing Large or Small Numbers

Sometimes scientists must use exceptionally large or small numbers. Scientific notation relies on exponents to write these numbers in a simpler way. For example, the large number 21,492 is 2.1492 x 10^{4} in scientific notation. This literally means 2.1492 x 10 x 10 x 10 x 10. To translate scientific notation into standard notation, you should move the decimal to the right the number of places indicated by the exponent. In the same way, the small number .067 is 6.7 x 10-2 in scientific notation. When the exponent is negative, you should move the decimal to the left to find the number in standard notation.

## Taking Measurements

One of the most common real world applications of exponents involves taking measurements and calculating multi-dimensional quantities. Area is the measure of space in two dimensions (length x width), so you always measure it in square units like square feet or square meters. For instance, when you calculate the area of a garden bed using feet, you should provide the solution in square feet or ft^{2} using an exponent.

Similarly, volume is the measure of space in three dimensions (length x width x height), so you always measure it in cubic units like cubic feet or cubic meters. For example, if you wanted to calculate the volume of a greenhouse, you would provide the answer in cubic feet or ft^{3} using an exponent.

While the concept of exponents can seem tricky at first, it is simple to see examples of exponents in the world around you. Learning how exponents function in real life is a good way to make it easier to understand them. And that's fantastic squared (fantastic^{2})!

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About the Author

Melissa Mayer is an eclectic science writer with experience in the fields of molecular biology, proteomics, genomics, microbiology, biobanking and food science. In the niche of science and medical writing, her work includes five years with Thermo Scientific (Accelerating Science blogs), SomaLogic, Mental Floss, the Society for Neuroscience and Healthline. She has also served as interim associate editor for a glossy trade magazine read by pathologists, Clinical Lab Products, and wrote a non-fiction YA book (Coping with Date Rape and Acquaintance Rape). She has two books forthcoming covering the neuroscience of mental health.