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If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

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If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink] New post 09 Feb 2012, 13:17
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If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36
[Reveal] Spoiler: OA
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Re: If (1/5)^{m} (1/4)^{18} = \frac{1}{2(10)^{35} [#permalink] New post 09 Feb 2012, 13:24
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If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36

Step by step:
(\frac{1}{5})^m*(\frac{1}{4})^{18}= \frac{1}{2*10^{35}} --> \frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2*2^{35}*5^{35}} --> \frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2^{36}*5^{35}} --> \frac{1}{5^m}= \frac{1}{5^{35}} --> m=35.

Answer: D.

Shortcut approach:
(\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*10^{35}} --> \frac{1}{5^m}* (\frac{1}{4})^{18} = \frac{1}{2*2^{35}*5^{35}} --> as there are only integers in the answer choices then we can concentrate only on the power of 5: they should be equal on both sides --> m=35.

Answer: D.
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Re: If (1/5)^{m} (1/4)^{18} = \frac{1}{2(10)^{35} [#permalink] New post 09 Feb 2012, 13:31
Thanks Bunnuel for the quick reply. So does that mean 1^m will always equal to 1? Because I was assuming m could be negative integer.
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Re: If (1/5)^{m} (1/4)^{18} = \frac{1}{2(10)^{35} [#permalink] New post 09 Feb 2012, 13:39
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink] New post 01 May 2012, 02:37
Thanks a lot for your prompt help!
This problem kept my thinking for more than one hour now!
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink] New post 01 May 2012, 02:52
Quote:
--> as there are only integers in the answer choices then we can concentrate only on the power of 5: they should be equal on both sides --> m=35.


@Bunuel: Can you give details on the short way? Why is it possible to concentrate only on the power of 5? :?:
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If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ? [#permalink] New post 02 Apr 2013, 06:58
steliossb wrote:
hey guys

this is the first question i got from the prep program and i am having trouble figuring it out:

(\frac{1}{4})^{18} * (\frac{1}{5})^{m} = \frac{1}{2*10^{35}}

find M


A) 17
B) 18
C) 34
D) 35
E) 36



any help will greatly be appreciated



4=2^2 => (1/2)^36*5^m=2*10^35

in order to get 10^35 you have to have 2^35*5^35. since we have 2^36, 2 will be left and the answer will be 2*10^35
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Re: I got this question on a Mock GMAT and I hate it so much [#permalink] New post 10 Aug 2013, 18:53
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sokenyou wrote:
(1/5)^m * (1/4)^18 = 1/2(10)^35

What is the value of m?

1. 17
2. 18
3. 34
4. 35
5. 36

I just don't get how to solve it using backsolving or picking numbers or something that is quick....I just hate it... :x


(\frac{1}{5})^m * (\frac{1}{2^2})^18= ( \frac{1}{(2*(2*5)^35})

(5^-1)^m * (2^-2)^18 = (2^-1 * 2^-35 * 5^-35)

5^(-m) * 2^(-36) = 2^(-36) * 5^(-35)

5^(-m) = * 5^(-35)

- m = -35

m = 35

Since you are asked to find the power of 5 i.e. m, you should be looking for 5 on the right hand side of the equation raised to some power. There is 10 on the denominator which is 2 * 5 raised to the power 35. The rest of the solution is rearranging to compare the powers of 5 on both sides.
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Last edited by hb on 10 Aug 2013, 19:07, edited 1 time in total.
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Re: I got this question on a Mock GMAT and I hate it so much [#permalink] New post 11 Aug 2013, 00:32
In these types of problems we can compare(qualize) the indices of the comparable variables.

a^m = a^n implies m=n

So the only term on the left hand side with five in it is 1/5 ^m
The only term on the right hand side with 5 in it is (1/10)^35

as 1/10 contains only one five so the resultant power on the right hand side is (1/5)^35

So equalizing comparable terms on both sides we get m = 35
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Re: I got this question on a Mock GMAT and I hate it so much [#permalink] New post 11 Aug 2013, 00:32
In these types of problems we can compare(qualize) the indices of the comparable variables.

a^m = a^n implies m=n

So the only term on the left hand side with five in it is 1/5 ^m
The only term on the right hand side with 5 in it is (1/10)^35

as 1/10 contains only one five so the resultant power on the right hand side is (1/5)^35

So equalizing comparable terms on both sides we get m = 35
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Exponents / powers [#permalink] New post 13 Mar 2014, 07:16
How can I approach this question? Why is the answer 'D'?

If (1/5)m(1/4)18 = 1/2(10)35, m?
a. 18
b. 17
c. 21
d. 35
e. 3
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Re: Exponents / powers [#permalink] New post 13 Mar 2014, 07:36
Expert's post
chrish06 wrote:
How can I approach this question? Why is the answer 'D'?

If (1/5)m(1/4)18 = 1/2(10)35, m?
a. 18
b. 17
c. 21
d. 35
e. 3


Merging similar topics. Please refer to the solutions above and ask if anything remains unclear.

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html


P.S. Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules #3 and 5. Thank you.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink] New post 14 Mar 2014, 01:09
Many thanks ! It's clear to me now :-)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?   [#permalink] 14 Mar 2014, 01:09
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