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I'm comparing Quantity A and Quantity B.

Column A
$15^{15} - 15^{14}$

Column B $15^{14}(14) - 1$

Since the 5 rules of exponents cant be applied, the book is asking me to factor quantity A and for the life of me, I dont understand. The book says quantity A, after factoring, should be $15^{15} - 15^{14} = 15^{14}(15-1)$. All the factoring examples have x's and y's so I'm having trouble finding where to start with this problem. Any tips?

YuiTo Cheng
  • 4,705
Jessica Jackson
  • 33
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    $15^{15} = 15^{14}\cdot 15$ – xxxxxxxxx Sep 28 '19 at 23:19
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    Just a comment about the x and y’s. The x’s and y’s are supposed to stand for numbers, so if there’s something you can do with x’s and y’s, you can also do that thing if the x’s and y’s are replaced with numbers. – Ovi Sep 28 '19 at 23:19
  • By the way, doing well on the GRE would be difficult for someone fresh out of Algebra. It would be an extreme pain for someone who isn’t that confortable with algebra. So if you’re in the latter froup, it might be worth it to spend several months just going through (part of) an algebra book from the beginning, ideally with someone to help you where you get stuck. – Ovi Sep 28 '19 at 23:27
  • Thank you! Math has never been my strong suit but the grad school I'm applying to doesnt factor in the math score as much as the others. That gives me a little relief. – Jessica Jackson Sep 29 '19 at 00:23
  • If $a,b>0$ and $a>b$ are positive integers then

    $$15^{a}-15^{b}=15^{b}15^{a-b}-15^{b}=15^{b}(15^{a-b}-1)$$

    which in your case $a=15$ and $b=14$ so that

    $$15^{15}-15^{14}=15^{14}15^{1}-15^{14}=15^{14}(15^{1}-1)$$

     – Axion004 Sep 29 '19 at 01:42

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