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Course: Arithmetic>Unit 17

Lesson 5: Intro to 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 $=$.
${2}^{5}$
${5}^{2}$

Want to join the conversation?

• is there a easier way of doing a very long exponents ?
• You can use the associative property of multiplication to group numbers.
For example:
3^6 = 3 x 3 x 3 x 3 x 3 x 3
If you do in one at a time: 3 x 3 = 9; 9 x 3 = 27; 27 x 3 = 81; 81 x 3 = 243; 243 x 3 = 729
Using grouping: (3 x 3) x (3 x 3) x (3 x 3) = 9 x 9 x 9 = 81 x 9 = 729

Hope this helps.
• why does math exist
• good question
• how do I express 144 in exponential form?
• 12^2 is the same as 12 * 12, or 144.
• im wrighting notes on my laptop but i cant figure out how to right it as 4 to the 3rd power with out completely typing a sentence out every time i use open office its the same thing basically as microsoft office
• for me you hold shift and press 6 so it would be 4^3
• why do we use exponents?
• Hey Aaron, exponents are just a faster (and easier) way to show repeated multiplication.
• bro im just trying to pass this school year, not pass away
• for real
• how are you supposed to write an exponent when your keyboard doesn't do that
• Use the carat symbol "^" (shift-6) on your keyboard.
For example: 5^3 is understood to be 5 to the power of 3.
Hope this helps.