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September 8th, 2014, 11:15 AM   #1
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Question 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.
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September 8th, 2014, 11:26 AM   #2
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You need an equation. 5^11 * (1/5^k) = ?
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September 8th, 2014, 11:27 AM   #3
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Oh, sorry I forgot the 5 at the end.

5^11 * (1/5^k) = 5
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September 8th, 2014, 11:33 AM   #4
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k = 10.
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September 8th, 2014, 11:35 AM   #5
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I need an explanation of how k can be equals to 10 thanks! But thanks so far.
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September 8th, 2014, 11:40 AM   #6
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5^11 * (1/5^k) = 5^11/5^k = 5 so 11 - k = 1, k = 10.
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September 8th, 2014, 12:02 PM   #7
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Question

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?
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September 8th, 2014, 12:14 PM   #8
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Quote:
Originally Posted by DecoratorFawn82 View Post

5^11 * (1/5^k) = 5

$\displaystyle \color{blue}{5^{11} \cdot \dfrac{1}{5^k} = 5
\\\;\\
\dfrac{5^{11}}{5^k}= 5^1
\\\;\\
5^{11-k} = 5^1
\\\;\\
11-k = 1
\\\;\\
k= 10 .}$
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September 8th, 2014, 12:22 PM   #9
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Quote:
Originally Posted by DecoratorFawn82 View Post
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?
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September 8th, 2014, 12:33 PM   #10
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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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