# Laws of Indices – Corbettmaths

In this video we’re going to look at laws of indices and we’re going to look at also indices up to the foundation paper. If you don’t jesusí higher i recommend you watch the video laws of indices advanced as well, so, first of all indices y ^, a times y ^ b, is equal to y ^, a plus b.

So you add the parts together! This really works! If you get the same base number so y +, 1, ok, let’s hope i can see why that works. So if we had y squared, we multiply that by y cubed well, y squared is y times y and y? Cubed is equal to y times y times y, and if we times these all together we’re going to have y times y times y times y times y, which should be equal to y to the power of 5, which is 5 of them, notice that, if you add the powers to +3, you get 5.

So that’s the first law of indices. Let’s have a look at some examples, so w to the power of 3 times w to the power of 5. We add the parts together to get w to the power of it? If we had a to the power of minus 2, we times that by a to the power of 5. Well again, you add the powers – 2, + 5.

Well, that’s free! so you get a cute and sometimes you have numbers in front of the letter. So something like this – y to the power of 6 times 5y to the power of 4! Well, let’s just multiply the two numbers together at the front so 2 times the 5 is equal to 10. Now, let’s add the powers for y, so y to the power of 6 times y to the power 4 or 6 plus 4.

Well, that’s also 10! So that’s would be 10 y to the power of 10. Okay, let’s have a look at the next load of indices, so the next law is, if we’re dividing. So if we have y to the power of air and we divided by y to the power of b, you take away, the parts would be y to the power of a minus b. Again, let’s have a look and see why that works. So if we add up y to the power of 5 and we divide that by y to the power of 3 or y to the power, 5 is y times y times y times y times y. We’re going to divide that by y cubed, which is y times y times y. Well, if we divide these, remember the if you divide a number about selfie at 1, so y divided by y is 1 y divided by y is 1 and y divided by y is 1, so we’re left with y times 1 on y times y is y squared, so notice that if you do 5 take away the 3 you get 2, which is our answer so notice that this reinforces the rule y to the power of a divided by y to the part b?

You take away the power to get y to the power of a minus b. Let’s have a look at some examples, so if we had something like w to the power of it, divided by w to the power of 2, you take away the power, so it take away. 2 is 6 is w to the power of 6? You could have something like this: a to the power of 4, divided by a to the power of 6, so 4 take away 6 wherefore, take away.

6 is minus 2, so the answer is a to the power of minus 2 and again sometimes you have numbers in front and also sometimes you have the divided by sign written as a line like so so. You could have something like this 24 w to the power of 6, divided by 2 w to the power of 2 or 2w squared and use divided. The numbers of the front versus also 24, divided by 2, is equal to 12 and then w to the 6, divided by w to the two you take away the power so you’re going to get w to the power of 4, so that would be 12 w to the power 4? Now that was elite, intent, interest and result y to the power of 0 is equal to 1? So any number to the power of 0 is always 1. Let’s just have a look and see why that’s the case. So if we had something like this y cubed divided by y cubed now we should know from basic number skills that if you divide something by itself, you get 1, but also using our previous law! What we’ve just looked at remember: if you’re dividing you take away the parts so 3 take away 3.

Well, that’s equal to y to the power of 0, so that means that y to the power of 0 will have to equal 1, and that just means, if you get any number to the power of 0, the answer is 1! So, for instance, if you get x to the power of 0, its 1, if you attend to the power of 0, is equal to 1. If you get 25 to the power, 0 is equal to 1, okay.

So any number to the power of zero is one another? Last law of indices. It’s a highlight because this one a part of a par or get a power of a power. So if we did y to the power of a all to the power of b, then the answer is y to the power of a b. That means u times the powers together, so that would mean it’s just an ellipse i’m pregnant. So if you’d y cubed- and then u squared that.

Well, u times the powers together, so it’d be y to the power of six again? Let’s just have a look at c1. So remember, squared means multiplied by itself, so we’re squaring y cubed? So we’re going to do y cubed times y cubed and if you add the powers together well, three plus three is six notice that if you do two times three times the two, it’s also six, so you just times the powers together and then that would give you the answer? So if you did something like this y to the power four all to the power of five and that would be y to the power of 20, so u times the powers together. The reason is, you could write. Y to the power 4 out 5 times and x, + 3 and add the powers together and then you’d get 20. Okay! You could also have something like this. You could have a to the power of 4 all to the power of minus 2, and can you times the powers together, so you’d get a to the power of minus here and also sometimes you make up numbers inside of the bracket, so it could be 2y, cubed and then squared and then what you do here is you take the number at the front and you do the power, so you we’re going to do 2 squared, which is 4, and then it’s y, and then you times the powers together, so that would be 3 times 2, which is 6. Let’s just do one more example like that? So like something like this 3y to the power 5 cubed or we’re going to do, 3, cubed well 3 times 3 times, 3 is 27, and then we times the parts together for the y so 5 times, 3 is 15? -, 20, 7 y to the power of 15. .