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## MAP Recommended Practice

### Course: MAP Recommended Practice>Unit 17

Lesson 10: Exponents

# Powers of fractions

Raising fractions to a power is a fundamental math skill. To do this, simply multiply the numerators and denominators separately. For example, when raising a fraction like 2/3 to the third power, multiply the numerators (2 × 2 × 2 = 8) and the denominators (3 × 3 × 3 = 27) to get the result 8/27. This method applies to all powers, making it easy to understand and apply. 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
• 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.
• where is the 1 coming from
• 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!
• At when Sal said let's go through more exponent examples, it sounded like he said let's go through s'more exponent examples😂
• IT did!
(1 vote)
• Why are there parenthesis surrounding the fraction? If you follow the order of operations PEMDAS, would you not treat the fraction as a division problem and do it first, then the exponent? In the example above, shouldn't it be written 2/3 cubed instead of (2/3) cubed?
• PEMDAS - The E = Exponents. They come before D = Division.
If you write 2/3 cubed (with the exponent 3 in superscript beside the fraction, the exponent would be on the 2 and you would end up with (2*2*2)/3 = 8/3

If you write 2/3 cubed with the exponent in superscript beside the 3, you end up with 2/(3*3*3) = 2/27

If you want to cube the entire fraction, the parentheses are required. (2/3)^3 = (2/3)(2/3)(2/30 = 8/27

Hope this helps.
• lil ah kids lol
• 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
• 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
• Why is 0.2 Times 0.2 = 0.04 and not 0.4?
• Because when you Do decimal times decimal you add the amount of places each decimal had to go to get to the right
• hello l tried typing 2/3^2 in a calculator and l got a different answer than 8/27 how come?
• 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.
• So the fast way is,
Numerator^exponent
Denominator^exponent

Place the answer in the orignal form.
• so short lol only

## 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.