Expert Tips for Converting Between Index and Expanded Forms

Index Notation Index Form to Expanded Form


Express the following in expanded form. So now we’re going in 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 means there are three lots of a’s. So if I write it as an expanded form, it should be a times a times a. So there are three a’s. Now b! a squared b! This one means there are two lots of a’s and three lots of b’s. It’s going to be times a, times b, times b, times b, okay? And then c! There are 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 are three a’s, four b’s, and one c. So we just expand it out like that.

So this one has two a’s, two a’s here and one b, one a, and one b. So it will be times a because there are 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 simply means there are three lots of twos. How do we write that? There are three lots of twos. It’s going to be two cubed, okay? So that’s what I mean: there are three factors of two or three lots of twos. There are three of the number two. Okay?

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

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

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