# Thread: Find 10^(k + 3)

1. ## Find 10^(k + 3)

Although I'm now in calculus, our professor wants to make sure that students do not forget the important topics of pre-calculus. To reach this goal, in addition to our calculus 1 homework, the professor adds one or two problems from pre-calculus as extra homework. Below is a problem that I worked on for about 15 minutes. Each time, I got the answer of 1000 but the correct answer is 500.

QUESTION:

If 10^(k) = 1/2, find 10^(k + 3)

How do I get 500 here?

2. Originally Posted by magentarita
Although I'm now in calculus, our professor wants to make sure that students do not forget the important topics of pre-calculus. To reach this goal, in addition to our calculus 1 homework, the professor adds one or two problems from pre-calculus as extra homework. Below is a problem that I worked on for about 15 minutes. Each time, I got the answer of 1000 but the correct answer is 500.

QUESTION:

If 10^(k) = 1/2, find 10^(k + 3)

How do I get 500 here?
$\displaystyle 10^{k+3}=10^k\times10^3$

$\displaystyle =\frac{1}{2}\times1000$

3. ## ok...

Originally Posted by mathaddict
$\displaystyle 10^{k+3}=10^k\times10^3$

$\displaystyle =\frac{1}{2}\times1000$
Of course, 1/2 times 1000 = 500

I thank you for the set up but here is what I did:

If 10^(k) = 1/2, find 10^(k + 3)

I multiplied both sides by denominator 2 to remove the fraction on the right side.

2(10^(k)) = 1

20^(k) = 1

At this point, I concluded that k has to be 0 because anything raised to the zero power = 1.

I then replaced k with zero for 10^(k + 3) = 10^3 = 1000

Did you follow what I did wrong?

4. $\displaystyle 10^(k+3)= 10^k \times 10^3 = \frac{1}{2} \times 1000$

2(10^(k)) = 1..........correct

20^(k) = 1....................This is not correct
Find the reason
.................

$\displaystyle 2(10^{k}) = {(2^\frac{1}{k} \times 10)}^k$

5. Originally Posted by magentarita
Of course, 1/2 times 1000 = 500

I thank you for the set up but here is what I did:

If 10^(k) = 1/2, find 10^(k + 3)

I multiplied both sides by denominator 2 to remove the fraction on the right side.

2(10^(k)) = 1

20^(k) = 1

At this point, I concluded that k has to be 0 because anything raised to the zero power = 1.

I then replaced k with zero for 10^(k + 3) = 10^3 = 1000

Did you follow what I did wrong?
Oh alright .

Note that 2(10^k) is NOT equal to 20^k . THat's a big mistake .