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 September 8th, 2014, 11:15 AM #1 Member   Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 Can't figure out the k exponent variable? Hi! I have a problem in my math book that says: Figure out the exponent k in the following equation a, 3^k * 3^4 = 3^9 k = 5 (5 + 4 = 9) c, (8^k)^3 = 8^18 k = 6 (6 * 3 = 18 ) b, 5^11 * (1/5^k) = 5 I have actually no idea about b?? I figured out a, c myself. But not b Please help! Last edited by DecoratorFawn82; September 8th, 2014 at 11:28 AM. September 8th, 2014, 11:26 AM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond You need an equation. 5^11 * (1/5^k) = ? September 8th, 2014, 11:27 AM #3 Member   Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 Oh, sorry I forgot the 5 at the end. 5^11 * (1/5^k) = 5 September 8th, 2014, 11:33 AM #4 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond k = 10. September 8th, 2014, 11:35 AM #5 Member   Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 I need an explanation of how k can be equals to 10 thanks! But thanks so far. September 8th, 2014, 11:40 AM #6 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 5^11 * (1/5^k) = 5^11/5^k = 5 so 11 - k = 1, k = 10. Thanks from DecoratorFawn82 September 8th, 2014, 12:02 PM #7 Member   Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 5^11 * (1/5^k) = 5^11/5^k = 5 so 11 - k = 1, k = 10. So the rule for figuring out the exponent variable is to: 1. Switch from multiplication to division 2. Divide the natural numbers (5/5 = 1). 3. Division for exponents is subtraction (11 - k = 1) 4. And then figure out k (11 - 10 = 1) Did I get it or not? September 8th, 2014, 12:14 PM   #8
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 Originally Posted by DecoratorFawn82 5^11 * (1/5^k) = 5

$\displaystyle \color{blue}{5^{11} \cdot \dfrac{1}{5^k} = 5 \\\;\\ \dfrac{5^{11}}{5^k}= 5^1 \\\;\\ 5^{11-k} = 5^1 \\\;\\ 11-k = 1 \\\;\\ k= 10 .}$ September 8th, 2014, 12:22 PM   #9
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Quote:
 Originally Posted by DecoratorFawn82 5^11 * (1/5^k) = 5^11/5^k = 5 so 11 - k = 1, k = 10. So the rule for figuring out the exponent variable is to: 1. Switch from multiplication to division 2. Divide the natural numbers (5/5 = 1). 3. Division for exponents is subtraction (11 - k = 1) 4. And then figure out k (11 - 10 = 1) Did I get it or not?

Can you explain step 2? September 8th, 2014, 12:33 PM #10 Member   Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 5^11 * (1/5^k) = 5 5^11 / (1 * 5^k) = 5 5^11 / 5^k = 5 The numbers 5/5 = 1 The exponents remaining 11 - k = 1 11 - 10 = 1 k = 10 OR: 5^11 * (1/5^k) = 5 5^11 / (1 * 5^k) = 5 5^11 / 5^k = 5 5^11-k = 5^1 k = 10 Tags exponent, figure, variable 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 drutledge Economics 0 June 21st, 2014 01:13 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 Al_Ch Elementary Math 2 May 21st, 2009 05:53 PM

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