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: 7,931 Thanks: 1125 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: 7,931 Thanks: 1125 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: 7,931 Thanks: 1125 Math Focus: Elementary mathematics and beyond 
5^11 * (1/5^k) = 5^11/5^k = 5 so 11  k = 1, k = 10.

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 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  
September 8th, 2014, 12:22 PM  #9  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,931 Thanks: 1125 Math Focus: Elementary mathematics and beyond  Quote:
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 5^11k = 5^1 k = 10 

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exponent, figure, variable 
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