I hope this message finds you well today. I did not recognize the set-up on this problem. Will you please throw some light on this?

#244

If .0015 x 10^m
.03 x 10^k = 5 x 10^7 , Then m-k?



a 9
b 8
c 7
d 6
e 5

Here is how I did it.

First, get rid of the decimals (by reducing the power of 10) and you end up with:

15 x 10^m-4
---------------- = 5 x 10^7
3 x 10^k-2

From here you can see how 15/3 gives you the 5 on the right side of the equation, so now solve for m and k by subtracting the powers and setting it equal to 7 (since you subtract exponents when dividing). This leaves you with:

m-4 -(k-2)=7 ...and so:

m-4-k+2=7 and,

m-k=9 which is A

Chirpy's method is, I think, the best and most efficient way to solve this problem.

However, if you are not good at exponents/radicals/the like, I suggest using trial and error. It will take longer, but you can get the correct answer without truly understanding exponents. Here is my method for those who are stuck and want to try the trial and error ways:

First, I would try to make the denominator a whole number. That would require k = 2, making the denominator 3. Then, I would see if answer a. works. For answer a. to be correct, m would have to equal 11 (m-2=9). This makes the numerator 150,000,000. So, what does 150,000,000 divided by 3 equal? 50,000,000! And that is exactly 5 x 10^7.

Lucky for us, answer a. was correct and this problem could be solved in under 2 minutes using trial and error.

Hope this helps!

Good work all! Though the "trial and error" approach is a good default method, I am chirping with "chirpy" on this one. Better to learn those rules of exponents so you can use them in future problems!