6th grade (Illustrative Mathematics)
Course: 6th grade (Illustrative Mathematics) > Unit 6Lesson 13: Lesson 13: Expressions with exponents
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.
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- hello I tried typing 2/3^2 in a calculator and I got a different answer than 8/27 how come(11 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.(30 votes)
- where is the 1 coming from(10 votes)
- The one means a whole. with the Identity property of Multiplication ,this doesn't change the product.(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)
- So the fast way is,
Place the answer in the orignal form.(4 votes)
- how does .9 to the power of 2 not equal 8.1?(1 vote)
- Remember the rules of multiplying decimals.
0.9 x 0.9
There are 2 decimal digits (1 in each number). So you answer needs 2 decimal digits.
0.9 x 0.9 = 0.81(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.(6 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.(4 votes)
- What if I have (2/3)^-2 which equals nine-fourths (9/4) Which is an improper fraction. Why don't I change this fraction into a mixed fraction?(2 votes)
- It would be a mixed number, not a mixed fraction. However, 9/4 and 2 1/4 are the same thing, so it may depend on the application that you are interested in. As a slope of linear function, 9/4 has much more meaning. Secondly, when typing answers into a computer, a particular program may not recognize a mixed number when it would a improper fraction.(3 votes)
- how will the 1 help(3 votes)
- why is sal putting a 1 in front(3 votes)
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.