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200^200*40^40/(20^20*400^400) =

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200^200*40^40/(20^20*400^400) =  [#permalink]

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New post 05 Jul 2018, 04:43
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A
B
C
D
E

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  45% (medium)

Question Stats:

68% (03:37) correct 32% (02:39) wrong based on 57 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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200^200*40^40/(20^20*400^400) =  [#permalink]

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New post 05 Jul 2018, 05:06
Bunuel wrote:
\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\)


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

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

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

D. \(1\)

E. \(2^{180}5^{180}\)



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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Re: 200^200*40^40/(20^20*400^400) =  [#permalink]

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New post 05 Jul 2018, 08:27
Bunuel wrote:
\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\)


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

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

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

D. \(1\)

E. \(2^{180}5^{180}\)


\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}\)
= \(\frac{(2^3*5^2)^{200}*(2^3*5)^{40}}{(2^2*5)^{20}(2^4*5^2)^{400}}\)
=\(\frac{2^{600}*5^{400}*2^{120}*5^{40}}{2^{40}*5^{20}*2^{1600}*5^{800}}\)
=\(2^{600+120-40-1600}*5^{400+40-20-800}\)
=\(2^{-920}*5^{-380}\)

Ans. A
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Re: 200^200*40^40/(20^20*400^400) =  [#permalink]

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New post 07 Jul 2018, 18:27
Bunuel wrote:
\(\frac{200^{200} 40^{40}}{20^{20}400^{400}}=\)


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

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

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

D. \(1\)

E. \(2^{180}5^{180}\)


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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Re: 200^200*40^40/(20^20*400^400) = &nbs [#permalink] 07 Jul 2018, 18:27
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