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# Exponent properties 1

## Video transcript

simplify three a times a to the fifth times a squared so the exponent property we can use here is if we have the same base in this case it's a if we have it raised to the X power and we're multiplying it by a to the Y power then this is just going to be equal to a to the X plus y power and we'll think about why that works in a second so let's just apply it here and let's start with the a to the fifth times a squared so if we just apply this property over here this will result in a to the 5 plus tooth power so that's what those guys reduce to or simplify to and then of course we still have we still have the 3 a out front now what I want to do is take a little bit of a side and realize why this worked let's think about what a to the fifth times a squared means a to the fifth a to the fifth literally means a times a times a times a times a now a squared literally means a times a a times a and we're multiplying the two times each other so we're multiplying these five A's times these two A's now what have we just done we're multiplying a times itself five times and then another two times five times and then another two times we are multiplying a times itself so let me make it clear this over here is a to the fifth this over here is a squared when you multiply the two you're multiplying a by itself you're multiplying a by itself seven times five plus two so this is a to the seventh power a to the five plus 2 power so this simplifies to three a times a to the seventh power a to the seventh power now you might say how do I apply the property over here what is the exponent on the a and remember if I just have an a over here this is equivalent to a to the first power so I can rewrite 3a as three times a to the first power and now it maybe make makes it a little bit clearer a to the first power and the Association property of multiplication I can do the multiplication of the A's before I worry about the 3s so I can multiply by these two guys first so a to the first times a to the seventh I just have to add the exponents because I have the same base and I'm taking the product that's going to be a to the 8th power and I still have this 3 out front so 3 a times a to the fifth times a squared simplifies to 3 a to the 8th power