What are exponents in math?

Exponents in plain words

An exponent is the small number written above and to the right of a base, and it tells you how many times to use that base in a multiplication. Written out, 3⁴ is a short way of saying 3 x 3 x 3 x 3.

The two parts have names: in 5² the 5 is the base and the 2 is the exponent. A square is a power with an exponent of 2, and you say a number squared; a cube is a power with an exponent of 3.

• 5² is 5 x 5, which is 25, so 25 is 5 squared.
• 4³ is 4 x 4 x 4, which is 64, so 64 is the cube of 4.
• 7⁰ is 1, because any nonzero number to the power 0 equals 1.
• 10³ is 1,000, because each step up the exponent adds one zero.

Zero is a special case rather than a count. Every nonzero base to the power 0 is 1, so learn it as a rule, the way you learned that anything multiplied by 0 is 0.

The slip worth naming is multiplying the base by the exponent: that gives 3 x 2 for 3², which is 6, when 3² is 3 x 3, which is 9. The exponent counts how many factors to use.

Negative and fractional exponents exist as well, and this page leaves them alone.

ETS lists basic concepts of exponents among the topics for the Mathematics subtest (5759), and an on-screen four-function calculator is provided on that subtest.

Why a paraeducator uses this in class

You read exponents long before you teach them. A science worksheet asks for a volume written as 10³ cubic centimeters, and somebody has to say out loud what the notation is asking for.

A power of ten is the quickest check you have on a number a student has written. Each step up the exponent adds a zero and moves every digit one place to the left, so the value gets ten times bigger.

Naming the parts settles an argument quickly. When a student can say that the base is 3 and the exponent is 4, what is left is a multiplication they can already do.

It also gives you something to point at. When a student writes 3 x 2 under 3² and gets 6, you can draw two threes and multiply them: 3 x 3 is 9, not 6.

Worked example

A small gym has 3 bleacher sections. Each section has 3 rows, and each row seats 3 students. Write the total as a power, then work it out.

1. Name the parts. The number used is 3 and the number of times is 3, so the base is 3 and the exponent is 3, and the total is 3³.
2. Read it as a multiplication. 3³ means 3 x 3 x 3, three factors of 3.
3. Multiply in pairs. 3 x 3 is 9, and 9 x 3 is 27.
4. The answer is 3 to the 3rd power, or 3^3, which seats 27 students.

Try a power of ten the same way. 10¹ is 10, 10² is 100, and 10³ is 1,000: one zero for every step up the exponent.

Practice questions

Continue learning

• Multiplication: the times tables and the strategies that make a small power quick.
• Measurement and units: metric and customary conversions, and the decimals that come with them.
• Geometry basics: area and volume, where a power of 3 turns up in a real measurement.

Try it on a full practice test

Once the notation feels routine, work through the free ParaPathways practice test.

Our study book covers every skill on both subtests, in English and Spanish.