Using the rules of exponents to simplify an expression. So what I have here are just four different expressions that I want to simplify using our rules of logarithms.
First one is our bases are the same and we are multiplying which tells us we have to add our exponents so what we end up with is y to the 4 plus 2 or y to the sixth.
Second example we are dividing, when we're dividing we end up subtracting and what I see is that my degree in the bottom, the power in the bottom is larger than the power on the top, so I actually know that I'm going to have to end up with a term in the bottom and then just 4 minus 7 is -3, the negative tells me this is in the bottom so it's just going to be x³. Another way of writing this if you want to deal with negative exponents could be x to the -3.
Third one is z to the third to the fifth, we have a power to a power, I know I have to multiply so what I end up with is z to the 3 times 5 which is just z to the 15th.
And the last one is we're dealing with expression to a power. This 4 has to get distributed in which tells me and then when I have the x² to the fourth, this has to be multiplied so ending up with x to the eighth and then we have y to the fourth stands alone. So using our rules of exponents to simplify an expression.