Imagine you need to multiply a number by itself over and over again. Writing out $4 \times 4 \times 4 \times 4 \times 4$ is a bit tedious. Mathematicians love shortcuts, so they came up with a cleaner way to write this: exponents.

This little expression means the exact same thing as the long multiplication problem above. It's just a compact way of saying "multiply 4 by itself 5 times." This notation has two key parts: the base and the exponent.

When you see an expression with an exponent, you'll often need to "evaluate" it. That's just a fancy way of saying you should do the multiplication to find the final value.

Let's try our first example, $4^5$.

Here are a few more. Notice how the value can grow very quickly.

For $2^3$, the base is 2 and the exponent is 3.

For $5^2$, the base is 5 and the exponent is 2. This is often read as "five squared."

A common mistake is to multiply the base and the exponent together. For example, it's easy to think $2^3$ equals $2 \times 3$, which is 6. But as we saw, the real answer is 8. Always remember that the exponent tells you about repeated multiplication, not a single multiplication.

Let's check your understanding of these new concepts.

Exponents are a fundamental building block in algebra and beyond. Getting comfortable with what they mean and how to evaluate them will set you up for success as you tackle more complex ideas.