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Lesson 1: Meaning of exponents

# Intro to exponents

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:
${4}^{3}$
The small number written above and to the right of a number is called an $\text{exponent}$. The number underneath the exponent is called the $\text{base}$. In this example, the base is $4$, and the exponent is $3$.
Here's an example where the base is $7$, and the exponent is $5$:
${7}^{5}$
An exponent tells us to multiply the base by itself that number of times. In our example, ${4}^{3}$ tells us to multiply the base of $4$ by itself $3$ times:
${4}^{3}=4×4×4$
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:
${4}^{3}=4×4×4$
$\phantom{{4}^{3}}=16×4$
$\phantom{{4}^{3}}=64$
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:
$2×2×2×2×2×2$
That's really long to write. My hands hurt just from typing it! Instead we can see that $2$ is multiplied by itself $6$ times. This means we can write the same thing with $2$ as the base and $6$ as the exponent:
$2×2×2×2×2×2={2}^{6}$
Cool, lets make sure we understand exponents by trying some practice problems.

## Practice set:

Problem 1A
Write $7×7×7$ using an exponent.

## Challenge set:

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