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## Pre-algebra

### Course: Pre-algebra > Unit 5

Lesson 3: Powers of fractions and decimals# Powers of fractions

Just like whole numbers with exponents, fractions are repeatedly multiplied. If you know how to multiply fractions, you're over half way there. Created by Sal Khan.

## Want to join the conversation?

- hello I tried typing 2/3^2 in a calculator and I got a different answer than 8/27 how come(12 votes)
- This is because of the order of operations. by typing 2/3^2, you told the calculator to calculate 2 divided by 3 to the power of 2, rather that 2/3 to the power of 2. The order of operations makes it that you calculate exponents before division. To get the right answer, you should input: (2/3)^2. Also (2/3)^2 is 4/9, not 8/27. That is (2/3)^3. Hope this helps.(34 votes)

- where is the 1 coming from(10 votes)
- I still don't get where the 1 is coming from. Why do you put it? I understand that one means a whole but still why do you decide to put 1? Thanks!(0 votes)

- Ok I want to know how the barnacles you got 2 x2x2 is 8 plz tell me I think you got it wrong and I want you to tell straight up that’s right or wrong because if 2x2x2 is 6 so plz don’t give us missed information(2 votes)
- 2x2x2 equals 8,and if I break it down

2x2 = 4

4x2 = 8

I see the confusion, but 2 to the power of 3 is 2 times itself 3 times, rather than just 2 x 3(7 votes)

- What is that carrot pointing up or down(1 vote)
- What are you asking? Are you talking about ^ which represents exponents when you cannot superscript the number? Do not know what a carrot pointing down V means except the shape of an absolute value function or shortcot for Velocity.(7 votes)

- hello l tried typing 2/3^2 in a calculator and l got a different answer than 8/27 how come?(2 votes)
- Do you mean 2/3^3?

If you typed it into the calculator as 2/3^3 the calculator will follow the order of operations so it will only cube the 3, if you want to cube the whole fraction you have to put parenthesis around the fraction like (2/3)^3 so that it will cube the whole thing.(5 votes)

- So the fast way is,

Numerator^exponent

Denominator^exponent

Place the answer in the orignal form.(4 votes) - why is sal putting a 1 in front(3 votes)
- Now I am the most recent question(3 votes)
- How would you do an exponent like this (1/2) 4(1 vote)
- It would actually be (1/2)^4(1 vote)

- how will the 1 help(2 votes)
- Like christian B. said, The one is to show that 0^0 or anything to the 0th power equals one. Because if you have 3^0 and you think about it as 0 threes you will get zero, instead if you put the one in front you will have 1 and zero zeros. (I legit just c/p what he wrote)(2 votes)

## Video transcript

Let's go through more
exponent examples. So to warm up, let's think
about taking a fraction to some power. So let's say I have
2/3, and I want to raise it to the
third power here. Now, we've already
learned there are two ways of thinking about this. One way is to say
let's take three 2/3's. So that's one 2/3, two
2/3's, and three 2/3's. So that's one, two, three, 2/3. And then we multiply them. And we will get-- let's
see, the numerator will be 2 times 2
times 2, which is 8. And the denominator's
going to be 3 times 3 times 3 times 3, which is equal to 27. Now, the other way of viewing
this is you start with a 1, and you multiply it
by 2/3 three times. So you multiply by 2/3
once, twice, three times. You will get the exact
same result here. So let's do one more
example like that. So lets say I had 4/9,
and I want to square it. When I raise something
to the second power, people often say,
you're squaring it. Also, raising something
to the third power, people sometimes say,
you're cubing it. But let's raise 4/9
to the second power. Let's square it. And I encourage you
to pause the video and work this out yourself. Well, once again,
you could view this as taking two 4/9's
and multiplying them. Or you could view this
as starting with a 1, and multiplying it
by 4/9 two times. Either way, your
numerator is going to be 4 times 4, which is 16. And your denominator
is going to be 9 times 9, which is equal to 81.