# Intro to exponents

CCSS Math: 6.EE.A.1
Learn how to use exponents and bases. For example, writing 4 x 4 x 4 x 4 x 4 with an exponent.
Here's what an exponent and a base look like:
$\blueD4^\goldD3$
The small number written above and to the right of a number is called an $\goldD{\text{exponent}}$. The number underneath the exponent is called the $\blueD{\text{base}}$. In this example, the base is $\blueD4$, and the exponent is $\goldD3$.
Here's an example where the base is $\blueD7$, and the exponent is $\goldD5$:
$\blueD7^\goldD5$
An exponent tells us to multiply the base by itself that number of times. In our example, $\blueD4^\goldD3$ tells us to multiply the base of $\blueD4$ by itself $\goldD3$ times:
$\blueD4^\goldD3 =\blueD4 \times \blueD4 \times \blueD4$
Once we write out the multiplication problem, we can easily evaluate the expression. Let's do this for the example we've been working with:
$\blueD4^\goldD3 =\blueD4 \times \blueD4 \times \blueD4$
$\phantom{\blueD4^\goldD3}= 16 \times 4$
$\phantom{\blueD4^\goldD3}= 64$
The main reason we use exponents is because it's a shorter way to write out big numbers. For example, let's say we want to express the following:
$\blueD2 \times \blueD2 \times \blueD2 \times \blueD2 \times \blueD2 \times \blueD2$
That's really long to write. My hands hurt just from typing it! Instead we can see that $\blueD2$ is multiplied by itself $\goldD6$ times. This means we can write the same thing with $\blueD2$ as the base and $\goldD6$ as the exponent:
$\blueD2 \times \blueD2 \times \blueD2 \times \blueD2 \times \blueD2 \times \blueD2 = \blueD2^\goldD6$
Cool, lets make sure we understand exponents by trying some practice problems.

# Practice set:

Problem 1A
Write $7 \times 7 \times 7$ using an exponent.

# Challenge set:

Problem 2A
Complete the inequality with $>, <,$ or $=$.
$2^5$
$5^2$