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Lots of exponents

This topic has 2 expert replies and 0 member replies
JJMforthegold Newbie | Next Rank: 10 Posts Default Avatar
Joined
29 Aug 2017
Posted:
5 messages

Lots of exponents

Post Sun Sep 17, 2017 3:45 pm
Experts-

Is there a fast way solve this without multiplying everything out?

(0.0015 x 10^m)/(0.03 x 10^k) = 5 x 10^7, then m - k =

a) 9
b) 8
c) 7
d) 6
e) 5
a

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Top Reply
Post Sun Sep 17, 2017 6:15 pm
JJMforthegold wrote:
Experts-

Is there a fast way solve this without multiplying everything out?

(0.0015 x 10^m)/(0.03 x 10^k) = 5 x 10^7, then m - k =

a) 9
b) 8
c) 7
d) 6
e) 5
Let k=0.
(0.0015 * 10^m) / (0.03* 10^0) = (5 * 10^7)

Convert the decimals to integers:
(15 * 10^(-4) * 10^m / (3 * 10^(-2) * 1) = (5 * 10^7)

Divide the integers and subtract the exponents:
5 * 10^(-2) * 10^m = 5 * 10^7

Cancel the 5's and divide each side by 10^(-2):
10^m = 10^9
m = 9.

Thus:
m-k = 9-0 = 9.

The correct answer is A.

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Post Sun Sep 17, 2017 4:24 pm
Quote:
if (0.0015 x 10^m) / (0.03 x 10^k) = 5 x 10^7, then m - k = ?

a. 9
b. 8
c. 7
d. 6
e. 5
Here's one approach:

First rewrite the equation as:
(0.0015/0.03) x (10^m)/(10^k) = 5 x 10^7
Simplify to get: (0.0015/0.03) x 10^(m-k) = 5 x 10^7

Aside: A quick way to simplify 0.0015/0.03 is to multiply top and bottom by 10,000 to get 15/300.
Simplify to get 1/20

So, we now have (1/20) x 10^(m-k) = 5 x 10^7
Isolate 10^(m-k) by multiplying both sides by 20 to get:
10^(m-k) = (20)(5) (10^7)
Simplify: 10^(m-k) = (100)(10^7)
Simplify: 10^(m-k) = (10^2)(10^7)
Simplify: 10^(m-k) = 10^9

So, m-k must equal 9

Answer: A

Cheers,
Brent

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