Exponential/power

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pmFollowed by: 6 members

by BTGmoderatorRO » Sun Nov 19, 2017 1:42 pm

$$2^{4x}=3600,\ what\ is\ the\ value\ of\ \ \left(2^{\left(1-x\right)}\right)^2$$

(A) -1/15
(B) 1/15
(C) 3/10
(D) -3/10
(E) 1
OA is b

I don't like indices and power question, i can't get this question right. Can any expert help me out on this?
Thank you so much

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Source: Beat The GMAT — Problem Solving | Sun Nov 19, 2017 1:42 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 19, 2017 2:04 pm

Roland2rule wrote:$$2^{4x}=3600,\ what\ is\ the\ value\ of\ \ \left(2^{\left(1-x\right)}\right)^2$$

(A) -1/15
(B) 1/15
(C) 3/10
(D) -3/10
(E) 1
OA is b

Given: 2^4x = 3600
Rewrite 2^4x and 3600 as follows: (2^2x)^2 = 60^2
We can conclude that 2^2x = 60

We want the value of: [2^(1-x)]^2
Apply power of a power rule to get: [2^(1-x)]^2 = 2^(2-2x)
Apply Quotient Law (in reverse) to get: 2^(2-2x) = (2^2)/(2^2x)
Evaluate numerator to get: (4)/(2^2x)
Replace 2^2x with 60 to get: (4)/(2^2x) = (4)/(60) = 1/15
Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8147; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Oct 17, 2019 7:24 pm

BTGmoderatorRO wrote:$$2^{4x}=3600,\ what\ is\ the\ value\ of\ \ \left(2^{\left(1-x\right)}\right)^2$$

(A) -1/15
(B) 1/15
(C) 3/10
(D) -3/10
(E) 1
OA is b

I don't like indices and power question, i can't get this question right. Can any expert help me out on this?
Thank you so much

Let's first simplify the expression we want to evaluate. We see that [2^(1-x)]^2 can be simplified as (2 * 2^(-x))^2 = 2^2 * 2^(-2x) = (2^2)/(2^(2x))

Thus, if we can determine 2^2x, then we have an answer.

Taking the square root of both sides of the given equation, which is 2^(4x) = 3600, we have 2^(2x) = 60; thus:

(2^2)/(2^(2x)) = 4/60 = 1/15

Answer: B

Scott Woodbury-Stewart
Founder and CEO
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