Main content

## Algebra basics

### Course: Algebra basics > Unit 1

Lesson 3: Exponents- Intro to exponents
- Exponent example 1
- Exponent example 2
- Squaring numbers
- Intro to exponents
- The 0 & 1st power
- Powers of zero
- Meaning of exponents
- 1 and -1 to different powers
- Comparing exponent expressions
- Exponents of decimals
- Powers of whole numbers
- Evaluating exponent expressions with variables
- Variable expressions with exponents
- Exponents review

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Exponent example 2

We can write a number multiplied by itself multiple times in exponential notation. 6 to the 8th power means we have 8 factors of 6, not that we multiply 6 by 8. 6 to the 8th power is a much larger number than 6 times 8. Created by Sal Khan.

## Want to join the conversation?

- Why is it 1 if the exponent is 0?(80 votes)
- The zero exponent is equal to 1 to satisfy a certain case in manipulating bases with exponents. When multiplying or dividing the same base with exponents we add or subtract the exponents:

To find the value of (3^3)(3^2) [the short form of (3 X 3 X 3) X (3 X 3) or (27)(9)] we add exponents to get 3^(3+2) or 3^5 with a value of 243.

To find the value of (3^3)/(3^2)[the short form of (3X3X3)/(3X3) or 27/9] we subtract exponents to get 3^(3-2) or 3^1 with a value of 3.

Now let us consider the case in which the two exponents are the same:

To find the value of (3^3)/(3^3) [the short form of (3X3X3)/(3X3X3) or 27/27 we subtract exponents to get 3^(3-3) or 3^0 whose value must equal the value of 27/27, or 1. To make the equation true 3^0 must equal 1.

The general case is: (x^a)/(x^b)=x^(a-b). When b=a, by substitution, this becomes (x^a)/(x^a)=x^(a-a)=x^0. Now let’s consider it another way. On the left side of the equation we have a division of the same numerator and denominator, which has a value of 1 (anything divided by itself equals 1). On the right side we have x^0. To make the equation true x^0 must equal 1.(8 votes)

- is there a way that someone knows how to do this easier(7 votes)
- woah that is a big question. let me read it before i answer(1 vote)

- lets say that my problem is 6 to the 8th power. is there a quicker easier way than doing 6*6*6*6*6*6*6*6 but not memory?(8 votes)
- Yes, there is.

What is 6 times 6? That's just 36, or 6^2.

36^4 is equal to 6^8.

Now, what is 36 times 36? That's 1296.

1296^2= 6^8

Now, we just have to multiply 1296 by itself.

The result is 1,679,616.(9 votes)

- I'm just wondering about the phrasing of exponents. At :23 seconds in the video, the way it is phrased is that 6 is multiplied by itself 8 times. That does not seem quite correct to me. 6^8th power multiplies 6 by 6 only 7 times and once by 1 times. Just being a stickler for words and their meaning but am I missing something? In other words, we start 1x6 and then x6x6x6x6x6x6x6. In short, the first 6 is simply six by itself not times 6, but fine, times one. Does this make sense or no?(6 votes)
- I was practicing some problems about the
**Pythagorean Theorem**and started off with the basics.

I know how to solve this problem, but when I checked their method, they did a different kind of*simplification*that I didn't understand.

I got to this point:`((17^2) - (8^2))`

But, instead just simplifying the powers and subtracting directly, they did this:`((17^2) - (8^2)) = (17 + 8) * (17 - 8)`

I know that their way is also right because we both got the same answer of**225**.

All I want to know is how they got from this:`((17^2) - (8^2))`

To this:`(17 + 8) * (17 - 8)`

Thanks so much for taking the time to read this, I*really*appreciate it!(4 votes)- Oh I get what you mean, it's something we call
**difference of squares**. Here's the fundamental principle used:

x^2 - y^2 = (x + y)(x - y)

In this case, x = 17 and y = 8, it's just something you can memorize to make life easier!

It's one of the multiple ways you can factor a quadratic, it's also very commonly seen.

Hope this helped :)

Happy holidays!!(4 votes)

- 6^8 = 1679616. precisely like wow that's huge!(5 votes)
- At0:16why are there so many sixes? I'm confused.(1 vote)
- Dear carla.

Those 6.6.6 represents 6X6X6. (multiplication between two numbers can also be denoted with "." instead of "X"). Please watch the video to completely understand about exponents(7 votes)

- How do you think about fractional or decimal exponents such as

2^0.3 ?(3 votes)- You would convert it into a fraction(0.3 = 3/10)

Then take the numerator and raise the base to it(2^3)

And you would square the value to the denominator

10sqrt(2^3)

As you see its very complex and you'll learn this later on(4 votes)

- OH I get it now!(3 votes)
- what is 0 to the 0th power?(2 votes)
- It is undefined. Why? Think of it as a paradox:

When 0 is raised to any number, it is zero

When any number is raised to the power of 0, it is one

So when you put those two together, it just doesn't make sense

So that is why...

Hope this helps(3 votes)

## Video transcript

Write 6 times 6 times 6 times
6 times 6 times 6 times 6 times 6 in exponential
notation. So what's going on over here? Well, we have 6 multiplied
by itself how many times? Let's see, that's 6 times 1,
then 6 times 2 is that. That's 6 times-- well,
it's not 6 times 2. It's 6 times itself two times. Remember, 6 times itself
two times would be 36. 6 times 2 would only be 12. So we have one 6, two 6, three
6, four 6, five 6's, six 6's, seven 6's, eight 6's. So we're multiplying 6 by
itself eight times. To write this in exponential
notation, we would say that this is equal to 6 to the
eighth power, which is literally equal to 6 times 6
times 6 times 6 times 6 times 6 times 6 times 6. Now, I want to make it very
clear this is NOT, this is NOT, this is NOT equal
to 6 times 8. 6 times 8 will only be 48. 6 to the eighth power is
a super huge number. 6 times 6 is 36, and you're
going to multiply that times 6, which is what? That's like 36 times--
that's what? 216, and you keep multiplying
it by 6, you get some huge number here. This number right here. It's worthwhile to point out
this number is huge. This number right here,
not so huge. It is not huge. So don't get confused. If you see 6 to the eighth
power, it's 6 times itself eight times, not 6 times 8.