How To Add Fractions With Negative Exponents

let's go through moreexponent examples. so to warm up, let's thinkabout taking a fraction to some power. so let's say i have2/3, and i want to raise it to thethird power here.

How To Add Fractions With Negative Exponents, now, we've alreadylearned there are two ways of thinking about this. one way is to saylet's take three 2/3's. so that's one 2/3, two2/3's, and three 2/3's.

so that's one, two, three, 2/3. and then we multiply them. and we will get-- let'ssee, the numerator will be 2 times 2times 2, which is 8. and the denominator'sgoing to be 3 times 3 times 3 times 3, which is equal to 27. now, the other way of viewingthis is you start with a 1, and you multiply itby 2/3 three times. so you multiply by 2/3once, twice, three times.

you will get the exactsame result here. so let's do one moreexample like that. so lets say i had 4/9,and i want to square it. when i raise somethingto the second power, people often say,you're squaring it. also, raising somethingto the third power, people sometimes say,you're cubing it. but let's raise 4/9to the second power. let's square it.

and i encourage youto pause the video and work this out yourself. well, once again,you could view this as taking two 4/9'sand multiplying them. or you could view thisas starting with a 1, and multiplying itby 4/9 two times. either way, yournumerator is going to be 4 times 4, which is 16. and your denominatoris going to be

9 times 9, which is equal to 81.