GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 27 Jan 2020, 23:32 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

Author Message
TAGS:

### Hide Tags

Director  P
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 717
Location: United States (CA)
Age: 40
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: Q168 V169 WE: Education (Education)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

Attached is a visual that should help.
Attachments Screen Shot 2016-04-05 at 10.29.41 PM.png [ 123.7 KiB | Viewed 2270 times ]

Intern  Joined: 14 May 2016
Posts: 4
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

Can someone please explain where the 1/2^36 is coming from?
Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1683
Location: India
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

sahmedmartinez wrote:
Can someone please explain where the 1/2^36 is coming from?

(1/5)^m * (1/4)^18 = 1 / (2 * (10)^35)

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

Two formulas are used here:
1. (a^m)^n = a^(mn)
2. a^m * a^n = a^(m + n)

=(1/5)^m * (1/2^36) = 1/(2^36 * 5^35)
Director  V
Joined: 05 Mar 2015
Posts: 964
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

Tessa8 wrote:
If $$([/5]^m [/4]^(18) = [/2(10)^(35)]$$ , then m = ?

a) 17
b) 18
c) 34
d) 35
e) 36

screenshot of question attached

(1/4)^18==[(1/2)^2]^18==(1/2)^36
also (1/10)^35==[1/(2*5)]^35

putting above both values in equation we get

(1/5)^m(1/2)^36=1/2*[1/(2*5)]^35
(1/5)^m(1/2)^36=[1/2]^36*(1/5)^35
cancelling 1/2^36 both sides
(1/5)^m=(1/5)^35

thus equating powers we get m=35

Ans D
Manager  G
Status: Not Applying
Joined: 27 Apr 2009
Posts: 178
Location: India
Schools: HBS '14 (A)
GMAT 1: 730 Q51 V36
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

(1/5)^m * (1/4)^18 = 1/(2*(10)^35)

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

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

For the two sides of the equation to be true, the powers of each base should be the same.

=> m = 35
_________________
http://www.wizius.in
Better Prep. Better Scores. Better Schools

Guaranteed Admission to Top-50 MBA Programs
You either get-in or get your money-back.
Director  D
Joined: 13 Mar 2017
Posts: 727
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

domu904 wrote:
If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

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

(1/5)^m * (1/4)^18 = 1/(2*(10)^35)
-> $$\frac{(1)}{(5^m*2^3^6)}=\frac{(1)}{(2^3^6*5^3^5)}$$
m = 35

Manager  B
Joined: 16 Jan 2017
Posts: 59
GMAT 1: 620 Q46 V29
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

Pretty straight forward. M=35. I fel like asking for what r is would be more challenging. As it would require to realise that 2 is to the power of 36, so r=18. Great question though! So this is a low 600 level question?
Director  D
Joined: 13 Mar 2017
Posts: 727
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

vmelgargalan wrote:
Pretty straight forward. M=35. I fel like asking for what r is would be more challenging. As it would require to realise that 2 is to the power of 36, so r=18. Great question though! So this is a low 600 level question?

Yes it is a pretty straight forward question and hence below 600 level question...

You can just solve the question in mind. Will not take more than 20 seconds.. Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

1
domu904 wrote:
If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

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

The negative exponent rule states: (1/a)^b can be re-expressed as a^(-b). Let’s flip all of the fractions using the negative exponent rule:

5^-m x 4^-18 = 2^-1 x 10^-35

5^-m x 2^-36 = 2^-1 x 2^-35 x 5^-35

5^-m x 2^-36 = 2^-36 x 5^-35

5^-m = 5^-35

m = 35

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  B
Joined: 21 Mar 2015
Posts: 8
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

I feel the question is pretty straight forward but ans was incorrect in many of the docs floating.

My take was

Left hand side denominator : 5^M
Right hand side denominator: 10^35 implies 5^35 * 2^35
So
M=35
Senior Manager  D
Joined: 18 Jun 2018
Posts: 250
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

domu904 wrote:
If $$(\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*(10)^{35}}$$, then m = ?

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

OA:D

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

$$(5)^{-m} * (2)^{-2*18} = 2^{-36}*(5)^{-35}$$

$$5^{-m} * 2^{-36}-2^{-36}*(5)^{-35}=0$$

$$2^{-36}(5^{-m}-5^{-35})=0$$

$$5^{-m}=5^{-35}$$

$$-m=-35$$

$$m=35$$
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4234
If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

Top Contributor
domu904 wrote:
If $$(\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*(10)^{35}}$$, then m = ?

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

Exponent property #1: $$(\frac{a}{b})^k=\frac{a^k}{b^k}$$

Exponent property #2: $$(b^x)^y = b^{xy}$$

Exponent property #3: $$(ab)^x = a^xb^x$$

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

Applying exponent property#1, we get: Given: $$(\frac{1^m}{5^m})(\frac{1^{18}}{4^{18}}) = \frac{1}{2*(10)^{35}}$$

Simplify to get: Given: $$(\frac{1}{5^m})(\frac{1}{4^{18}}) = \frac{1}{2*(10)^{35}}$$

ASIDE: To determine the value of m, we must rewrite both sides of the equation with similar base.
So, for the left side, we'll rewrite $$4$$ as $$2^2$$
For the right side, we'll rewrite $$10$$ as $$2 \times 5$$

We get: $$(\frac{1}{5^m})(\frac{1}{(2^2)^{18}}) = \frac{1}{2*(2 \times 5)^{35}}$$

Applying exponent property#2, we get: $$(\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{2*(2 \times 5)^{35}}$$

Applying exponent property#3, we get: $$(\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{2*(2^{35})(5^{35})}$$

Since $$2*(2^{35} = 2^{36}$$, we can write: $$(\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{(2^{36})(5^{35})}$$

NOTE: Notice that I really didn't need to spend so much time working on the powers of 2, since the variable m was the exponent of 5.
Had I focused solely on the powers of 5, I could have answered the question MUCH faster.

That said, I wanted to show all of the exponent properties at work. Cheers,
Brent
_________________ If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?   [#permalink] 09 Aug 2019, 09:49

Go to page   Previous    1   2   [ 32 posts ]

Display posts from previous: Sort by

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