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## 6th grade (Illustrative Mathematics)

### Unit 6: Lesson 15

Lesson 15: Equivalent exponential expressions# Intro to exponents

CCSS.Math:

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:

The small number written above and to the right of a number is called an start color #e07d10, start text, e, x, p, o, n, e, n, t, end text, end color #e07d10. The number underneath the exponent is called the start color #11accd, start text, b, a, s, e, end text, end color #11accd. In this example, the base is start color #11accd, 4, end color #11accd, and the exponent is start color #e07d10, 3, end color #e07d10.

Here's an example where the base is start color #11accd, 7, end color #11accd, and the exponent is start color #e07d10, 5, end color #e07d10:

An exponent tells us to multiply the base by itself that number of times. In our example, start color #11accd, 4, end color #11accd, start superscript, start color #e07d10, 3, end color #e07d10, end superscript tells us to multiply the base of start color #11accd, 4, end color #11accd by itself start color #e07d10, 3, end color #e07d10 times:

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:

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:

That's really long to write. My hands hurt just from typing it! Instead we can see that start color #11accd, 2, end color #11accd is multiplied by itself start color #e07d10, 6, end color #e07d10 times. This means we can write the same thing with start color #11accd, 2, end color #11accd as the base and start color #e07d10, 6, end color #e07d10 as the exponent:

Cool, lets make sure we understand exponents by trying some practice problems.

## Practice set:

## Challenge set:

## Want to join the conversation?

- 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(5 votes)
- for me you hold shift and press 6 so it would be 4^3(8 votes)

- why do we use exponents?(5 votes)
- Hey Aaron, exponents are just a faster (and easier) way to show repeated multiplication.(31 votes)

- why does math exist(12 votes)
- To bore people to death.(12 votes)

- it doesnt show it as correct when i type 1 when the exponent is 0 even though my teacher taught us that it will always be 1.(10 votes)
- how are you supposed to write an exponent when your keyboard doesn't do that(8 votes)
- 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.(5 votes)

- what is 5 to the third power(6 votes)
- Thank you it did help @ks0607(8 votes)
- How do you find out what 4x4x4 is becus3e i got 48 but it says 64(5 votes)
- first you do 4 times 4 which is 16 then 16 times 4 which is 64(5 votes)

- what is 1000000 to the 3rd power? How do u figure out those big type of exponent questions if you get them(5 votes)
- 1000000000000000000(3 votes)

- is there a easier way of doing a very long exponents ?(2 votes)
- There are log and exponent tables out there. I don't know if your curriculum allows for them, but they're pretty common in math textbooks.(5 votes)