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Good day students welcome to mathgotserved.com in this clip were going to be going over to properties of exponents what are going to be doing in this presentation is we going to be taking a look at 11 properties of exponents Hooghly the first of all look at the formula and that can see there are algebraic and then the numerical example let's take a look at the first property which is the product of powers property okay so the formula is as follows and in this presentation would on the right and on the formulas the assumption is that X and Y are real numbers in the powers M and in represent integers okay so the formula the sold let's say we have X to the and times X to the and him the product of powers property just simply tells the debt when you multiply and exponents of the same base you simply add the powers alright so there goes the formula let's consider two examples the firsts will be algebraic example a let's say we have X to the third power times X to the fourth power according to the product of powers property of exponents you multiply to exponents with the same base you simply out the powers exited 3+4 your final result is X to the seven power out of the site notes before we start example be if you like be to get the printable copy of the properties of exponents included in the formula algebraic and numerical example just look in the comments section the comments section below on the description a you should find a link now take you two a Google doc containing the properties okay alright let's take a look at the be part a number medical example so what if we have to to the third power times two to the fourth power in this case will going to have if we apply the product of powers property we simply have the powers to to the 3+4 which is to to the seven power and then you can work this out with your calculator two to the seven power is 100 and swing T now let's move on to property number two this is the power of the product if you take a look at the name he can basically guess what the property will look like in this case we raise in the product some factors so certain power right so the formula is as follows if you have a product let's the XY where X and Y are real numbers recent the M where and is an integer power of a product property basically tells you that you can distributes the power to the existing powers of the factors in the product okay so us and there's a one here the one here as your existing powers to the fourth power is non-is specified you end up with X to the and power times the Y to the and power now let's go see there are some examples the first one will be algebraic example a let's say you have XY square three's to the third power now can enter the power product property will simply going to distribute is three to both powers X over how power so it's one so just in a distributed okay so that gives us X to the third power Y to the sixth power so you have three times one and why to the 2×3 to have X to the third power times why to the sixth power that's what you gets when you apply the power product property to on algebraic expression of this nature Arcos either example be what it we have to times three raised to the second power not if you want to do this Om use of the order of operations you take a look at the parenthesis you multiply these two get six and then you read it to the power to 62nd power is 30 60 let's take a let's apply the power only product property here so since two and three don't have any specified powers you can use of find one that's that the four power there now according to the power product property we can distribute this power to these existing powers so we're going to have two to the two times one which is to times three to the two times one which is also two so another have to square is 4×3 square which is 94 times9 is 36 that's exactly what we expected the answer to be positive on to property number three the third property is the power a power okay let's take a look at will the formula looks like so let's see you have a power X to the and where X is the real number and M is an integer raised to the power and what the power power property of exponents as you can do is that you can simply multiply the powers you have X MN okay so that's the power only power our property of exponents in this is highlighted in example number two think a look another of the another example here on algebraic example let's say we have X to the third power raised to the second power what it is going to be

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