My Math Forum Can't figure out the k exponent variable?

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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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Quote:
 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

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