Tyler York

June 12, 2023

In this video, Achievable GRE course author Matt Roy explains how to solve a seemingly tedious exponents problem with ease. This video is a great review for multiple exponent rules.

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00:00:02 In this problem, you will be using almost all of the exponent rules to find the answer. First of all, you should notice that all of the answers are three to some power. That should give you a hint that when you simplify the expression, you should simplify everything to a base of three. So for example 81 is 9 ^2. 00:00:28 Which is equivalent to 3 ^2 * 3 squared. So 81 should be replaced with three to the 4th power. The nine in the denominator should be replaced with three squared. And now you can simplify the entire expression by using your exponent rules. So 3 to the 4th power to the 4th power is 3 to the 16th power, because you multiply the exponents when there's an exponent outside of an exponent. 00:00:56 In the denominator, 3 squared to the 4th power again means you multiply the exponents, so then you are left with three to the 8th power. When you multiply 2 numbers that have the same base and a different exponent, you add the exponents. So then we're left with three to the third power times 3 to the 8th power, which would be 3 to the 11th power, and again the rule for division. 00:01:23 Is that you subtract the exponents when the bases are the same. So we have 3 to the 16th power on the top and three to the 11th power on the bottom. You subtract the exponents and you are left with three to the fifth power.

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