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Bunuel
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200^200*40^40/(20^20*400^400) = 05 Jul 2018, 04:43
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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77% (03:06) correct 23% (02:47) wrong based on 714 sessions

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\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\)


A. \(\frac{1}{2^{920}5^{380}}\)

B. \(\frac{1}{2^{240}5^{240}}\)

C. \(\frac{1}{2^{180}5^{180}}\)

D. \(1\)

E. \(2^{180}5^{180}\)
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A
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GMAT Focus 1: 735 Q90 V89 DI81
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200^200*40^40/(20^20*400^400) = 05 Jul 2018, 05:06
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Bunuel
\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\)


A. \(\frac{1}{2^{920}5^{380}}\)

B. \(\frac{1}{2^{240}5^{240}}\)

C. \(\frac{1}{2^{180}5^{180}}\)

D. \(1\)

E. \(2^{180}5^{180}\)
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separate the 10s and convert 4 also in terms of 2..

\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\frac{(2*10^2)^{200} (2^2*10)^{40}}{(2*10)^{20}(2^2*10^2)^{400}}=\frac{2^{200}*10^{400}*2^{80}*10^{40}}{2^{20}*10^{20}*2^{800}*10^{800}}=\frac{2^{200+80} 10^{400+40}}{2^{820}10^{820}}=\frac{1}{2^{(820-280)}*10^{(820-440)}}=\frac{1}{2^{(540+380)}5^{380}}\)

A
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200^200*40^40/(20^20*400^400) = 05 Jul 2018, 08:27
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Bunuel
\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\)


A. \(\frac{1}{2^{920}5^{380}}\)

B. \(\frac{1}{2^{240}5^{240}}\)

C. \(\frac{1}{2^{180}5^{180}}\)

D. \(1\)

E. \(2^{180}5^{180}\)
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\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}\)

= \(\frac{(2^3*5^2)^{200}*(2^3*5)^{40}}{(2^2*5)^{20}(2^4*5^2)^{400}}\)

=\(\frac{2^{600}*5^{400}*2^{120}*5^{40}}{2^{40}*5^{20}*2^{1600}*5^{800}}\)

=\(2^{600+120-40-1600}*5^{400+40-20-800}\)

=\(2^{-920}*5^{-380}\)

Ans. A
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200^200*40^40/(20^20*400^400) = 07 Jul 2018, 18:27
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Bunuel
\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\)


A. \(\frac{1}{2^{920}5^{380}}\)

B. \(\frac{1}{2^{240}5^{240}}\)

C. \(\frac{1}{2^{180}5^{180}}\)

D. \(1\)

E. \(2^{180}5^{180}\)
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If we re-express all of the factors to have bases of 10, 20, or 40, we can cancel and simplify the expression.

[20^200 x 10^200 x 40^40]/[20^20 x 40^400 x 10^400]

[20^180]/[10^200 x 40^360]

We can re-express 40^360, obtaining:

[20^180]/[10^200 x 20^360 x 2^360]

1/[10^200 x 20^180 x 2^360]

1/[10^200 x 10^180 x 2^180 x 2^360]

1/[10^380 x 2^540]

1/[5^380 x 2^380 x 2^540]

1/[5^380 x 2^920]

Answer: A
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200^200*40^40/(20^20*400^400) = 06 Jan 2019, 19:25
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What a great question! The key here is not to get scared by high powers. By looking at the answer choices you can most likely figure out that it is asking you to break the big numbers down into powers of 2 and powers of 5!
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200^200*40^40/(20^20*400^400) = 06 Jan 2019, 20:33
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Bunuel
\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\)


A. \(\frac{1}{2^{920}5^{380}}\)

B. \(\frac{1}{2^{240}5^{240}}\)

C. \(\frac{1}{2^{180}5^{180}}\)

D. \(1\)

E. \(2^{180}5^{180}\)
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Just remember \((m*n)^x\) => \(m^x * n^x\)
and continue expanding the term to the simplest form and voila you will get the answer

Will solve each part individually, so that the solution can be understood clearly.
\(200^{200} 40^{40}\) -(x)
=> \((2^3 * 5^2)^{200} * 2^{120} * 5^{40}\)
=> \(2^{600} * 5^{400} * 2^{120} * 5^{40}\)
=> \(2^{720} * 5^{440}\)

\(20^{20}400^{400}\) -(y)
=> \((2^2 * 5)^{20} * (2^4 * 5^2)^{400}\)
=> \(2^{40} * 5^{20} * 2^{1600} * 5^{800}\)
=> \(2^{1640} * 5^{820}\)


\(\frac{x}{y}\) = \(\frac{1}{2^{1640-720} * 5^{820-440}}\)
\(\frac{x}{y}\) = \(\frac{1}{2^{920}5^{380}}\)

Correct answer A.
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200^200*40^40/(20^20*400^400) = 10 Oct 2024, 07:12
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Since the powers of 2 are different for all given options, one can save time by just finding the power of 2 in the question and choosing (A) :)
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200^200*40^40/(20^20*400^400) = 17 Nov 2025, 08:07
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