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Rules for Rational Exponents - Problem 1
Simplifying a rational expression with fractional exponents and basically these rules are the exact same that you remember which is still my fractions instead of whole numbers, so whenever we are dividing, what you have to remember is that this translates into subtraction, bases are the same we're dividing then subtract.
So this turns into a to the 1/4th minus 2/3. When we're subtracting we need a common denominator, in this case we're looking at the denominators 4 and 3, so our denominator is 12. This needs to be multiplied by 3 over 3 and 4 over 4, so we end up with 8 3/12 minus 8/12 which is 8 to the -5/12.
Sometimes you're asked that you need to express something with positive exponents, so you need to remember that a negative exponent is just basically putting the term in the denominator so this would turn into 1 over 8 to the 5/12.
So that is dividing, very similar to multiplication, remember we have our bases that are same and we're multiplying, we add our exponents, so the same thing holds even if we have fractional exponents. Bases are the same multiply that just turns into addition. Adding fractions again we need common denominator in this case our denominator is 6, so we need to multiply the first thing by 3 over 3, the second by 2 over 2 leaving us with 5 to the 3/6 plus 4/6 add them up, 5 to the 7 over 6.
So just because we're dealing with fractional exponents doesn't mean anything's changed. We still have to subtract when we divide, add when we multiply, everything is exactly the same, don't let the fractions scare you one bit.