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 Your Progress

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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

13 Jan 2018, 06:01

2

Top Contributor

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

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

Show Tags

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 \(y^4=\frac{10000}{2^2}=\frac{10^4}{2^2}....y=\frac{10}{\sqrt{2}}=5\sqrt{2}\)