In this lesson on algebra exponents are covered. Get information and algebra exponents practice here.
Exponents are numbers that have been multiplied by themselves. For instance, 3 · 3 · 3 · 3 could be written as the exponent 34: the number 3 has been multiplied by itself 4 times.
Exponents are useful because they let us write long numbers in a shortened form. For instance, this number is very large:
But you could write it this way as an exponent:
It also works for small numbers with many decimal places. For instance, this number is very small but has many digits:
It also could be written as an exponent:
Scientists often use exponents to convey very large numbers and very small ones. You'll see them often in algebra problems too. Watch this short video from Khan Academy to learn more about what exponents are and how to calculate them.
As you saw in the video, exponents are written like this: 43 (you'd read it as 4 to the 3rd power). All exponents have two parts: the base, which is the number being multiplied; and the power, which is the number of times you multiply the base.
Because our base is 4 and our power is 3, we’ll need to multiply 4 by itself three times.
43 = 4 ⋅ 4 ⋅ 4 = 64
Because 4 · 4 · 4 is 64, 43 is equal to 64, too.
Occasionally, you might see the same exponent written like this: 5^3. Don’t worry, it’s exactly the same number—the base is the number to the left, and the power is the number to the right. Depending on the type of calculator you use—and especially if you’re using the calculator on your phone or computer—you may need to input the exponent this way to calculate it.
How would you simplify these exponents?
Don’t feel bad if you’re confused. Even if you feel comfortable with other exponents, it’s not obvious how to calculate ones with powers of 1 and 0. Luckily, these exponents follow simple rules:
That’s it! If you’re curious about why those rules work, this video from Khan Academy gives a good explanation.