LESSON: Powers and Exponents

READ: Writing the Product of a Repeating Factor as a Power

Writing the Product of a Repeating Factor as a Power

In the last section, we took bases with exponents and wrote them out as factors. We can also work the other way around. We can take repeated factors and rewrite them as a power using an exponent.

Example

$7 \times 7 \times 7 = \underline{\;\;\;\;\;\;\;}$

There are three seven’s being multiplied. We rewrite this as a base with an exponent.

$7 \times 7 \times 7 = 7^3$

Example

$11 \times 11 \times 11 \times 11 = 11^4$

We can also find the value of a power by evaluating it. This means that we actually complete the multiplication and figure out the new product.

Example

5^2

We want to evaluate 5 squared. We know that this means $5 \times 5.$ First, we write it out as factors.

$5^2 = 5 \times 5$

Next, we solve it.

$5^2 = 5 \times 5 = 25$

RED ALERT!!! The most common mistake students make is to just multiply the base times the exponent.

$5^2$ IS NOT $5 \times 2$

The exponent tells us how many times to multiply the base by itself.

$5^2$ is $5 \times 5$