### Video instructions and help with filling out and completing How Form 8815 Index

**Instructions and Help about How Form 8815 Index**

Hi good luck changing to and from third full by which I mean this question what the cube root of x that's third for a third is a way of depicting an irrational number and we're gonna 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 I'll show that again question 2 the fifth root of x is X to the one-fifth fraction one over means it's a root now what about if the the surd itself is raised to a power I give an example the fourth root of x cubed well an index form that's going to be x over X to the power minus take now the denominator of the fraction is the root we're finding but this time the numerator at the top number have been one it's going to be the power to which X is raised if you think about it's part of our laziness as I call it in maths strictly speaking each of those is X to the power 1 and since one over three give another example of that question four the seventh root of x to the power of five equals x to the well because we've got roots involved SERDES we know it's going to be a fraction the denominator is the 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 five it's one other one we need to know reciprocals what about one over x squared well we write that as X to the power two look X to the power two here but because it's one over it's a reciprocal we put a minus in front so it's X to the minus two minus means a reciprocal question six goes through that again 1 over X to the power 7 equals so we write X to the power 7 and because it's 1 over a reciprocal we put a minus in front now for more examples to look at what about if it's sort of being 1 over something and Poupon one under something it's a number the X is under the power of X is under I'll give an example 5 X cubed 5 over X cubed we write as 5x cubed and because X is part of the denominator what we do is put minus sign there it's 5 X cubed but what about if the denominator expression has a coefficient I'll give you an example 3 over 7 x squared equals well here we treat the numbers as our coefficient so it's going to be 3 over 7x squared and because X the denominator we put a minus in front so it's 3/7 X to the minus 2 another way would be to write this it's 3 X to the minus 2 all over 70 I think you'll find in practice when you're doing calculus 3/7 X to the minus 2 be the easier way to write it now we're just going to combine all of those for our last few examples 8 over the square root of x well we start by looking at the denominator we've got the square root the second root of x so we write that's X to the 1/2 we've got an 8 as a numerator but because X is part of the denominator I finished by putting a minus sign in front and then our last one question Tenace combine all of these things 7 over 5 cube root x squared right let's take it slowly cube root of x squared I write as X the denominator is the root we're trying to find so it's over three the numerator is this two here the power to which X was raised it's part of the denominator of the terms we put the minus in front and then what do we got left coefficient it's seven over five so 7 over 5 X to the minus 2/3 right nothing I repeat nothing beats practice so I'm going to put 11 up here I want you to turn them to index 4 but if you're out there trying to design them but one more exam right might cop them down press pause and come okay let's go through the answers then question eleven see right X to the minus three its denominator and put the numerator nine in front now here we've got the eighth root of x to the power of 5 so it's eight sorry so this X to the denominator is a numerator is 5 here we've got us to the denominator the part that contains X we've got X to the 3/5 it's a part of the denominators to put a minus in front and two in front because that's what multiplying by that's the numerator in the whole term here we've got let's do the X first we've got square root of x it's part of the denominators to put a minus in front and then we had a four and a night that's the coefficient question 15 doesn't really matter what order we do this in I suppose it's more logical to do the coefficient first so we've got 3 over 8 there's the coefficient we've got X to the power 5 and it's part of the denominator of the term so there's a minus in front here well the top this approach for the second one its 2/5 X to the power 7 R but hang on X we're dividing by its reciprocal path the denominator in the terms it's - here we've got X to the power 4 throat so my index has a denominator of 4 and the numerator of