How to Multiply Two Variables That Are Raised to a Fraction

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Multiplying two variables that are raised needs to be done in a very specific way to make sure your answer is accurate. Multiply two variables that are raised with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Algebra


Video Transcript

Hi, my name is Marija. I'm a mathematician, and today I'm going to show you how to multiply variables that have fractional exponents. So if I have the expression A to the 1/4th power times A to the 2/4ths power, what I'm going to do is just follow the multiplication law of exponents which tells me that if my base is the same I'm going to keep that base and I'm going to add the exponents. So I'm doing A to the 1/4th plus 2/4ths and actually that should go in parentheses, so 1/4th plus 2/4ths is 3/4ths and that becomes A to the 3/4ths power. Now when you have a fraction as an exponent, you can simplify this further because this is going to become the fourth root of A to the cube power and the way that I did, or I'm sorry, to the third power. The way that I did it was take the denominator, make it become your root and then keep your base and make the numerator become your new exponent inside of the radical. So I have the same base, I kept it, I added my fraction exponents and then I rewrote it in root form. And then the only difference you might have is you might have different denominators in which case you have to remember how to add fractions and get a least common denominator first. My name is Marija and I just showed you how to multiply variables with fractional exponents.