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-   -   Can't figure out the k exponent variable? (http://mymathforum.com/algebra/46259-cant-figure-out-k-exponent-variable.html)

 DecoratorFawn82 September 8th, 2014 11:15 AM

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

 greg1313 September 8th, 2014 11:26 AM

You need an equation. 5^11 * (1/5^k) = ?

 DecoratorFawn82 September 8th, 2014 11:27 AM

Oh, sorry I forgot the 5 at the end.

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

 greg1313 September 8th, 2014 11:33 AM

k = 10.

 DecoratorFawn82 September 8th, 2014 11:35 AM

I need an explanation of how k can be equals to 10 thanks! But thanks so far.

 greg1313 September 8th, 2014 11:40 AM

5^11 * (1/5^k) = 5^11/5^k = 5 so 11 - k = 1, k = 10.

 DecoratorFawn82 September 8th, 2014 12:02 PM

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?

 aurel5 September 8th, 2014 12:14 PM

Quote:
 Originally Posted by DecoratorFawn82 (Post 205391) 5^11 * (1/5^k) = 5

$\displaystyle \color{blue}{5^{11} \cdot \dfrac{1}{5^k} = 5 \\\;\\ \dfrac{5^{11}}{5^k}= 5^1 \\\;\\ 5^{11-k} = 5^1 \\\;\\ 11-k = 1 \\\;\\ k= 10 .}$

 greg1313 September 8th, 2014 12:22 PM

Quote:
 Originally Posted by DecoratorFawn82 (Post 205399) 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?

 DecoratorFawn82 September 8th, 2014 12:33 PM

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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