you that when you have x to the N power that's equivalent to 1/x to the POS n right so let's see how we can utilize this formula to help us so first of all let's take a look at this one x to the -2 so if we use the formula this is just saying 1/ X pos2 and we're done okay let's take a look at another example we've got 1 over y -3 now when you look at this you could simplify it as saying okay y the3 That's 1 over y pos3 but then when we divide by a fraction it's the same thing as taking the numerator and then multiplying by the reciprocal because dividing is the same thing as multiplying by the reciprocal right so this is really like multiplying by y cubed over one all I do was take the denominator and flip it now when we multiply we get y Cub over 1 which is just y cubed now that's a lot of work and that's absolutely not necessary all you have to do is when you see a negative exponent okay or a quantity with a negative exponent all you have to do is just move it to the other side of the fraction bar so if it's a negative and it's down in the denominator go ahead and move it into the numerator and make it a positive exponent same thing with this one you could think of x^ -2 as over one anything divided by one is itself so by moving this to the denominator and making it a positive exponent you've taken care of that negative exponent so you just want positive exponents in your final answer so let's look at some more challenging examples like this one over here so what you can do is just like when you simplify fractions ordinarily you can look at the numbers okay just like a fraction and integers and you can just simplify this like two goes into 2 once two goes into 8 four times so we've just reduced this to 1/4 right and then just like we were talking about earlier we've got x to the -3 let's move that to the other side of the fraction bar and make that x to the positive3 here we've got Z to the ne -2 let's move that to the numerator and make that Z to the pos2 and then y the 5th that already has a positive exponent so we're just going to leave it where it's at in the numerator y 5th now just one quick note a lot of times when students see the negative exponent they think to themselves oh that makes the number negative and you don't want to make the number negative you just want to take the reciprocal so to show you another example along that same lines like say for example if you had uh 2x^ -2 y Cub all to the -3rd power right so what you could do is you could take this -3 and you're going to distribute it okay to each of these terms now this is just a monomial just one term so you just raise everything to that3 power now you don't see it but this is really like 2 to the first power power to a power we multiply so 1 * -3 gives you 23r okay2 * 3 gives you x 6 and 3 * -3 gives you y to the 9th now all we have to do is think of that as being divided by one anything over one or divided by one is itself so now anything that has a negative exponent we're just going to move it to the other side of the fraction bar and make it a positive exponent so this is going to end up being uh let's see x 6 over 2 to the 3 power y the 9th power 2 cubed is 2 * 2 * 2 3 * so that comes out to x 6 over 8 y 9th okay let's look at one more example this one here same thing we're going to work with the numbers we're going to work with the X's together as a group and we're look at the Y's together as aoup group so here we're just going to reduce these we can see that 2 goes into 50 25 times 2 also goes into 12 six times we've reduced it okay now here when you divide you subtract so you take the numerator power minus the denominator power so -7 - 4 which is1 and you put that result in the numerator okay so this is the quotient rule when you divide you subtract the exponents same thing here with the y -2 - -3 is like adding three so that's going to be y to the 1st okay so we're almost done but we just want positive exponents in that final answer so we're going to take this quantity here we're going to move it to the other side of the fraction bar so that gives us 25 y to the 1st or you could just say y okay divid 6 x to the 11th power and that's your final answer so we just have positive exponents we reduced as much as we we could there and that's it so I hope this helped you to understand how to work with negative exponents a little bit more efficiently and easily subscribe to the channel check out some more math videos on my channel Mario's math tutoring uh YouTube channel and I look forward to seeing you in the future videos I'll talk to you soon