# Writing Equivalent Algebraic Expressions For Multiplication and Division 04:14 minutes

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Transcript
**Writing Equivalent Algebraic Expressions For Multiplication and Division**

It’s Saturday night and Morton waits for his friend and competitor, Manfred, to join him in his mom's basement. Manfred shows up to once and for all settle their lifetime-long competition in the royal and most honorable discipline of... Stamp collecting! How do you compete at stamp collecting? The collector with the most precious stamps wins. First, they reorder their collection. Then, they cancel out like-stamps. Reordering and canceling out like stamps is similar to a math property we can use when using the Quotient of Powers Property. Let's see how they do that with their stamp collections. Each angelfish stamp is represented with the letter ‘a’. For a barracuda stamp, we use the letter ‘b'. And, for a conch stamp, we use the letter ‘c’. See how like-variables cancel each other out? To apply the Quotient of Powers Property for like bases, the base stays the same and simply subtract the exponent in the denominator from the exponent in the numerator. Remember, this only works for like-bases. Bases are the number or variable that is multiplied by itself and the exponent is the smaller number above that tells us how many times to multiply the base by itself. Any base raised to the 1st power is equal to the base. Let's try this problem. Just like we did with the stamps, we can cancel out the like-variables. The simplified expression is equal to 'a'. Now let’s use the Quotient of Powers Property to simplify the same expression. For like-base 'a', we can subtract the exponent in the denominator from the exponent in the numerator, so 'a' is raised to the '2 minus 1' power, which is equal to 'a' raised to the first power, or just 'a'. Let’s use the Quotient of Powers Property to simplify another expression. First, let’s write this expression as a fraction. Remember, the fraction bar is another math symbol that indicates division. To make it easier to solve, let’s reorder the equation to put like-parts together. Then, for the like-bases, subtract the exponent in the denominator from the exponent in the numerator. Let's do one more problem. Oh, this problem looks very complicated. Naah, we can do it! Just use your math rules and properties! First, remember that when dividing by a fraction, just multiply by the reciprocal. Remember, to find the reciprocal of a fraction, just switch the position of the numerator and denominator. First, multiply the two numerators and the two denominators together. Next, rewrite the equation to separate the numerator and denominator into fractions with like-terms. Coefficients with coefficients, x's with 'x's, and 'y's with 'y's, and finally, apply the Quotient of Powers Property. Let's get back to Morton and Manfred and the duel of the stamps. The stamp competition is going down to the wire and Morten has a surprise move. He breaks out his most precious stamp: the red lobster. Oh no!

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