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If 2^(8x) = 640000, then what is the value of 2^(2x−2)?

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If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

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If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

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Bunuel wrote:
If \(2^{(8x)} = 640000\), then what is the value of \(2^{(2x−2)}\)?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160


\(2^{(8x)} = 640000 = 2^6*10^4\)
\(2^{(2x)} = 2^{6/4}*10^{4/4}\)
\(2^{(2x)} = 2^{3/2}*10\)
\(2^{(2x)} = 2\sqrt{2}*10 = 20\sqrt{2}\)

\(2^{(2x-2)} = 20\sqrt{2}/4 = 5\sqrt{2}\)

Hence Option A is correct
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Last edited by 0akshay0 on 22 Feb 2017, 21:29, edited 1 time in total.
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Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

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New post 22 Feb 2017, 05:59
In the step

2^(2x)=20√2 is OK

Now
2^(2x−2)=2^(2X) / 2^2 = 20√2 / 4 = 5√2 :?:
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Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

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New post 12 Jan 2018, 17:41
Bunuel wrote:
If \(2^{(8x)} = 640000\), then what is the value of \(2^{(2x−2)}\)?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160


what was your approach to this Bunuel because I'm not quite following the posted solution. Thanks!
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Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

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New post 12 Jan 2018, 23:20
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rnz wrote:
Bunuel wrote:
If \(2^{(8x)} = 640000\), then what is the value of \(2^{(2x−2)}\)?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160


what was your approach to this Bunuel because I'm not quite following the posted solution. Thanks!



Step 1:

\(2^{(8x)} = 640000\);

\((2^{2x})^4 = 2^{10}*5^4\);

\(2^{2x} = 2^{(\frac{5}{2})}*5\);

\(2^{2x} = \sqrt{2^5}*5\);

\(2^{2x} = 20\sqrt{2}\).


Step 2:

\(2^{(2x−2)}=\frac{2^{(2x)}}{2^2}\).



Step 2:

Substitute \(2^{2x} = 20\sqrt{2}\) into \(\frac{2^{(2x)}}{2^2}\).:

\(\frac{20\sqrt{2}}{2^2}=5\sqrt{2}\).


Answer: A.

Hope it's clear.
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Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

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New post 12 Jan 2018, 23:22
Bunuel wrote:
If \(2^{(8x)} = 640000\), then what is the value of \(2^{(2x−2)}\)?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160


Similar questions to practice:
https://gmatclub.com/forum/if-3-6x-8-10 ... 98777.html
https://gmatclub.com/forum/if-3-6x-810- ... 54347.html

8. Exponents and Roots of Numbers



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Hope it helps.
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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 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

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New post 13 Jan 2018, 06:01
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Bunuel wrote:
If \(2^{(8x)} = 640000\), then what is the value of \(2^{(2x−2)}\)?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160


Another approach:

Given: 2^(8x) = 640000
Raise both sides to the power 1/2 (aka take square root of both sides) to get: [2^(8x)]^(1/2) = 640000^(1/2)
Simplify to get: 2^(4x) = 800
Raise both sides to the power 1/2 (again) to get: [2^(4x)]^(1/2) = 800^(1/2)
Simplify: 2^2x = √800
Simplify: 2^2x = 20√2
Divide both sides by 2² (aka 4) to get: (2^2x)/2² = (20√2)/4
Simplify both sides to get: 2^(2x - 2) = 5√2

Answer: A

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If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

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New post 13 Jan 2018, 06:22
Bunuel wrote:
If \(2^{(8x)} = 640000\), then what is the value of \(2^{(2x−2)}\)?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160



Another approach, although most of these approaches is solving the equation..

Let \(2^{(2x−2)}=y\), so \(y^4=2^{(2x−2)*4}=2^{8x-8}=\frac{2^{8x}}{2^8}=\frac{640000}{2^6*2^2}=\frac{10000}{2^2}\)
so \(y^4=\frac{10000}{2^2}=\frac{10^4}{2^2}....y=\frac{10}{\sqrt{2}}=5\sqrt{2}\)

A
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If 2^(8x) = 640000, then what is the value of 2^(2x−2)?   [#permalink] 13 Jan 2018, 06:22
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