LESSON: Powers and Exponents

READ: Whole Numbers, Powers, Bases and Exponents

Whole Numbers, Powers, Bases and Exponents

In the past two lessons you have been working with whole numbers. A whole number is just that. It is a number that represents a whole quantity. Today, we are going to learn about how to use exponents. Exponents are very powerful little numbers. They change the meaning of the whole number as soon as they are added.

Here is an example.

The large number is called the base. (You can think about the base as the number that you are working with.)

The small number is called the exponent. (The exponent tells us how many times to multiply the base by itself.)

An exponent can also be known as a power.

We can read bases and exponents.

EXAMPLES:

$3^5$ is read as three to the fifth power.

$2^7$ is read as two to the seventh power.

$5^9$ is read as five to the ninth power.

We use the number with the power in all cases except two. When you see a base with an exponent of 2 or an exponent of 3, we have different names for those. We read them differently.

$2^2$ is read as two squared.

$6^3$ is read as six cubed.

It doesn’t matter what the base is, the exponents two and three are read squared and cubed.

What does an exponent actually do? An exponent tells us how many times the base should be multiplied by itself.

Examples:

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

$5^{10} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5$