Index Notation: Index Form to Expanded Form


Express the following in expanded form. So now we’re going the opposite direction. This time they give you the index form and we’re going to change it or convert it to an expanded form like a fully spread out form. So a cube that means there’s three lots of a’s. So if I write it as an expanded form, it should be a times a times a. So there’s three a’s. Now b! a squared b! This one means there’s two lots of a’s and three lots of b’s. It’s going to be a times a times b times b times b, okay? And then c! There’s three lots of a’s, four lots of b’s, and one c and one three. So keep the three there’s only one of them. There’s three a’s, four b’s, and one c. So we just expand it out like that.

So this one two a’s, two a’s here and one b, one a, and one b. So it will be a times a because there’s two a’s in the front plus five times two a’s and one b minus two and one a and one b. Make sure you’re multiplying them.

Three factors of two. This just simply means there’s three lots of twos. How do we write that? There’s three lots of twos. It’s going to be two cubed, okay?So that’s what I mean there’s three factors of two or three lots of twos. There’s three of the number two. Okay?

Write x factors of 5 in index form. x factors of 5 mean there’s x amounts of 5. I don’t know what x is so I just left it as a pronumeral. So there’s x amounts of 5 which means we don’t know how many so I’ll just write it as a dot dot, so five times five times however amount of fives there are. There’s x of them. So it should be five to the power of x because it’s x factors of five.

So some people tend to get it the wrong way around. So make sure you’re clear with the right where the base goes and where the indices go, okay? So the indices or the index, the power gives you how many of that number.


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