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Rules for Rational Exponents - Problem 2
Simplifying an expression with rational exponents, so let's simplify an expression with fractional exponents is pretty much the exact same thing as simplifying an expression without. We just need to use the rules of exponents in order to simplify this equation up.
So what we have is a expression here with xs and ys all to a power. There's a couple of ways of doing this. The first thing we could do would be combine our xs if we wanted, or we can distribute this 12 in to each term beforehand, it doesn't really matter just pick one and go with it.
What I see is I see all our denominators are factors of 12, so if I distribute this 12 and I actually get rid of all my fractions which makes my life easier, so I'm going to go ahead and distribute that 12 and first if you wanted to combine your xs first, that would be okay as well.
So this 12 comes into every single term and remember when you're taking a power to a power we have to multiply, so x to the 1/2 to the twelfth becomes x to the sixth. Y to the 2/3 to the 12, remember again power to power multiply, so 2/3 times 12 is 24 over 3 which is just going to be y to the eighth and then x to the twelfth there's no power to multiply, so we just end up with x to the twelfth.
So by distributing this 12 we ended up getting rid of all our fractions, combining like terms, we can combine our xs, when we're dividing we subtract, so x to the sixth minus 12, x and -6, negative is going to put on the bottom, so we end with y to the eighth over x to the sixth.
So dealing with rational exponents is pretty much exactly the same as dealing with normal exponents, you're just dealing with a fractions instead of whole numbers.