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### Instructions and Help about How Form 8815 Index

Hi, good luck changing to and from third! Full stops are needed to separate each sentence. By "third full", I mean this question: what is the cube root of x? The cube root is a way of depicting an irrational number, and we're going to express it in index form. Index form means you have the symbol we're using for the unknown and a power or index. Now, it's a root, so it's 1 over something, and it's the cube root, so it's 1 over 3. If the index is a fraction, it means there's a root. Let me show that again. Question 2: The fifth root of x is x to the one-fifth, which means it's a root. Now, what about if the surd itself is raised to a power? I'll give an example: the fourth root of x cubed. In index form, that's going to be x over X to the power minus 3. Now, the denominator of the fraction is the root we're finding, but this time, the numerator at the top number has been one. It's going to be the power to which X is raised. If you think about it, it's part of our laziness, as I call it in math. Strictly speaking, each of those is X to the power 1, and since one over three, give another example of that. Question 4: The seventh root of x to the power of five equals x to the 5/7. Well, because we've got roots involved, we know it's going to be a fraction. The denominator is the root we're trying to find, in this case the seventh root, and the numerator is the power of X within the root symbol. Question 5: One other one we need to know is reciprocals. What about one over x squared? Well,...