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 May 15th, 2015, 05:12 PM #1 Member   Joined: May 2015 From: U.S.A. Posts: 45 Thanks: 0 How do you simplify a two-variable division problem with variables in the exponent? Simplify $\displaystyle \frac{x^{3a+2}} {x^{2a-1}}$ (In case I'm doing the LaTeX incorrectly, it's (x^3a+2) / (x^2a-1), or (x to the power of 3a + 2) divided by (x to the power of 2a - 1) Since there's no answer to the problem, I wouldn't know how to set up a logarithm for either part of the fraction. (Sorry for how basic my knowledge is. I'm working on it.) The answer is $\displaystyle x^{a + 3}$, but I can't see how to get there. Last edited by skipjack; May 18th, 2015 at 11:16 PM. May 15th, 2015, 05:16 PM   #2
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 Originally Posted by Rexan Simplify $\displaystyle \frac{x^{3a+2}} {x^{2a-1}}$ Since there's no answer to the problem, I wouldn't know how to set up a logarithm for either part of the fraction. (Sorry for how basic my knowledge is. I'm working on it.) The answer is $\displaystyle x^{a + 3}$, but I can't see how to get there.
Exponents have two properties that are useful here.

1) $\displaystyle \frac{1}{m^n} = m^{-n}$

2) $\displaystyle m^n \cdot m^p = m^{n + p}$

So
$\displaystyle \frac{x^{3a + 2}}{x^{2a - 1}} = \left ( x^{3a + 2} \right ) \cdot \left ( x^{-(2a - 1)} \right ) = x^{(3a + 2) - (2a - 1)}$

etc.

-Dan

Last edited by skipjack; May 18th, 2015 at 11:17 PM. May 15th, 2015, 05:24 PM   #3
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Quote:
 Originally Posted by topsquark Exponents have two properties that are useful here. 1) $\displaystyle \frac{1}{m^n} = m^{-n}$ 2) $\displaystyle m^n \cdot m^p = m^{n + p}$ So $\displaystyle \frac{x^{3a + 2}}{x^{2a - 1}} = \left ( x^{3a + 2} \right ) \cdot \left ( x^{-(2a - 1)} \right ) = x^{(3a + 2) - (2a - 1)}$ etc. -Dan
Finally got it. Thank you! Tags division, exponent, problem, simplify, twovariable, variables Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post cduinctk714 Algebra 3 December 8th, 2014 07:21 PM DecoratorFawn82 Algebra 17 September 10th, 2014 03:59 PM Bencz Algebra 4 May 4th, 2013 04:14 PM claudiomalk Algebra 2 November 9th, 2012 08:52 PM skarface Algebra 1 January 24th, 2010 03:28 PM

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