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Hi there and welcome to another video from Hegarty mats it's mr. Haggerty here and in this video we're talking about index form our second video on the topic where we focus in on powers of 0 and of 1 so let's start by looking at some index form tables that we completed on video 1 so previously I asked you to complete the power tables for powers of 2 powers of 3 powers of 4 and powers of 5 so please go back to index form video 1 if you didn't do that because it's gonna make this video and the subsequent ones so much better if you have done that so in this particular video what are we going to be focusing on while we're focusing on anything to the power of 1 okay and anything to the power of 0 so 2 to the 0 3 to the 0 4 2 0 5 to 0 can you spot what the answer is always 4 anything to the power of 0 can you spot what the answer is always 4 anything to the power of 1 well hopefully you can see anything to the power of 1 2 to the power of 1 just gives you two back 3 to the power of 1 just gives you three back four to the 1 gives you 4 back 5 to the 1 gives you 5 back that's so straightforward that's obvious 2 to the 1 means 2 multiplied by itself once easy now 2 to the 0 students sometimes think that 0 based on the patterns we've discovered previously anything to the 0 is 1 2 to the 0 is 1 3 to the 0 is 1 4 to the 0 is 1 5 2 zeros want Bob to the zeros 1 cap to the zeros 1 anything to the power of 0 gives you 1 okay right let's take this forward then let's write a rule the power of 0 rule any number to the power of 0 gives 1 always for example 7 to the 0 is 1 negative 2 to the 0 is 1 1 point 3 7 to the power of 0 gives 1 okay and the power of 1 rule this can be useful you'll be surprised when we do some algebra later any number to the power of 1 gives itself gives the same number back so 7 to the 1 is 7 negative 2 to the 1 is negative 2 and 1 point 3 7 let's say to the 1 is 1 point 3 7 and if they're in our head that's going to be useful to us in future work so let's do some questions right evaluate the following that means work the answer out 7 to the 0 anything to the zero is 1 5 to the power of 1 is just itself 5 10 to the 0 is 1 3 to the 1 is 3 2 to the 0 is 1 negative 2 to the 0 anything to the 0 is 1 that's right zero point 7 to the 1 just gives you back zero point 7 20 3381 to the one is 27,000 381 three million five hundred twenty-five thousand three hundred eighty seven to the zero that's just one and negative six point three to the one is negative six point three okay nice and easy stop okay I'd like you to pause and try and write the following in index form well we've got a five multiplied and we've also got a nine multiplied one time two time three time four times five times six time now we could write this as 5 multiplied by 9 to the power of 6 but we were explicitly asked to write that in index form so we should write the 5 as 5 to the power of 1 that's right so just be careful there write that in index form to always write the smaller number first write the base number of 5 before 9 it's just good practice write the next one what have we got on the go here we've got a 3 that's multiplied by itself three times we've got ourselves a 7 multiplied by itself once and we've got an 8 multiplied by itself three times so let's put them in base number order and remembering to write them in index form so we're going to write that as 3 to the power of 3 multiplied by 7 to the power of 1 that's right good and then lastly multiplied by 8 to the power of 3 last one I'm sure you can do without coloring in this is just going to be equal to 2 cubed multiplied by 7 to the power of 1 and we're done next fill in the missing number pause the video and have a go 7 to the what gives you 1 it's gotta be 0 7 to the walk gives you 7 it's got to be 1 & 7 to the walk gives you 49 that's from previous videos hopefully you realize - 7 squared is equal to 49 nice and easy there I just want to finish with a power table again just for you to practice this I can't tell you how useful it is to have this type of thing in your head and be good at it for the future videos that are coming so could you fill in the missing gaps in that table well from this video 7 1 is just 1 7 multiplied by itself and the answer is 7 7 0 well anything 0 is just 1 so I'm just going to put a 1 here and a 1 here now I just want you to spot what's going on here because our next video do you remember the powers are going down from 3 to 2 to 1 to 0 to negative 1 to negative 2 as we're

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