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Hi everyone, in this we are going to solve 2 to the power of 18 minus 1 equals what?

We are going to write it as 2 to the power of 9 times 2 is 18.

So we can write it like this 2 to the power of 9 times 2 is 18 minus 1 so what have we used here a to the power of n whole to the power of m is equal to a to the power of n times m so here you have the product of the power so you can split it in this way now what does it look like this is in a form of an identity a square minus b square which is equal to a plus b times a minus b now we're gonna solve for that so we have 2 to the power of

minus 1 and then as we know 2 to the power of 9 is equal to 512 so we're going to substitute that 512 plus

so now we are just gonna split this both into into

times 500 plus 11 and now we're gonna use the FOIL method and multiply the 2 brackets so we have 500 times

times 11 500 times 13, so we're going to write it like this, plus 500 multiplied by 13 plus 11 and then the last term plus 13 times

plus 143 now let's just add them up together so we have

so when you add them up you get 341262 So you have the answer of


Speaker 0: Hi everyone, in this we are going to solve 2 to the power of 18 minus 1 equals what? So first of all we

Speaker 1: are going to split this. We are going to write it as 2 to the power of 9 times 2 is 18. So we know that

Speaker 0: 9

Speaker 1: times 2. So we can write it like this 2 to the power of 9 times 2 is 18 minus 1 so what have we used here a to the power of n whole to the power of m is equal to a to the power of n times m so here you have the product of the power so you can split it in this way now what does it look like this is in a form of an identity a square minus b square which is equal to a plus b times a minus b now we're gonna solve for that so we have 2 to the power of

Speaker 0: 9

Speaker 1: plus 1 times 2 to

Speaker 0: the power of 9

Speaker 1: minus 1 and then as we know 2 to the power of 9 is equal to 512 so we're going to substitute that 512 plus

Speaker 0: 1

Speaker 1: times 512 minus 1 so 512 plus 1 is

Speaker 0: 513

Speaker 1: and 512 minus 1 is

Speaker 0: 511

Speaker 1: so now we are just gonna split this both into into

Speaker 0: 500

Speaker 1: plus

Speaker 0: 13

Speaker 1: times 500 plus 11 and now we're gonna use the FOIL method and multiply the 2 brackets so we have 500 times

Speaker 0: 500

Speaker 1: so we're going to write that

Speaker 0: 500

Speaker 1: times

Speaker 0: 500

Speaker 1: then we have

Speaker 0: 500

Speaker 1: times 11 500 times 13, so we're going to write it like this, plus 500 multiplied by 13 plus 11 and then the last term plus 13 times

Speaker 0: 11.

Speaker 1: Now 500 times plus

Speaker 0: 250, 000

Speaker 1: plus 500 times 24 is just

Speaker 0: 12, 000

Speaker 1: plus 143 now let's just add them up together so we have

Speaker 0: 250, 000

Speaker 1: plus

Speaker 0: 12, 000

Speaker 1: plus

Speaker 0: 143

Speaker 1: so when you add them up you get 341262 So you have the answer of

Speaker 0: 2

Speaker 1: to the power of 18 minus 1 is equal to

Speaker 0: 262, 143.

Speaker 1: Thank you so much for watching. Hope this is helpful. Bye bye. Take care.

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Norway Math Olympiad Question | You should be able to solve this!