In this lesson on algebra exponents are covered. Get information and algebra exponents practice here.

### What are exponents?

**Exponents** are numbers that have been multiplied by themselves. For instance, **3 · 3 · 3 · 3** could be written as the exponent 3^{4}: 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:

1,000,000,000,000,000,000

But you could write it this way as an exponent:

10^{18}

It also works for small numbers with many decimal places. For instance, this number is very small but has many digits:

.00000000000000001

It also could be written as an exponent:

10^{-17}

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.

#### Understanding exponents

As you saw in the video, exponents are written like this: 4^{3} (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.

4^{3} = 4 ⋅ 4 ⋅ 4 = 64

Because **4 · 4 · 4** is 64, **4**^{3} 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.

#### Exponents to the 1st and 0th power

How would you simplify these exponents?

7^{1} 7^{0}

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:

**Exponents with a power of 1**

Any exponent with a power of **1** equals the **base**, so 5^{1} is 5, 7^{1} is 7, and x^{1} is *x*.**Exponents with a power of 0**

Any exponent with a power of **0** equals **1**, so 5^{0} is 1, and so is 7^{0}, x^{0}, and any other exponent with a power of 0 you can think of.

That’s it! If you’re curious about why those rules work, this video from Khan Academy gives a good explanation.