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0.8^(-5)/0.2^(-4) =

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0.8^(-5)/0.2^(-4) = [#permalink]

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New post 10 Sep 2017, 05:33
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A
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E

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  25% (medium)

Question Stats:

70% (01:23) correct 30% (01:24) wrong based on 27 sessions

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Kudos [?]: 128688 [0], given: 12182

BSchool Forum Moderator
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Re: 0.8^(-5)/0.2^(-4) = [#permalink]

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New post 10 Sep 2017, 06:42
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\(\frac{0.8^{(-5)}}{0.2^{(-4)}} = \frac{0.2^{(4)}}{0.8^{(5)}} = \frac{0.2*0.2*0.2*0.2}{0.8*0.8*0.8*0.8*0.8} = \frac{1}{4*4*4*4*0.8} = \frac{10}{4*4*4*4*4*2} = \frac{5}{4^5} = \frac{5}{1024}\)(Option A)
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Kudos [?]: 258 [0], given: 546

0.8^(-5)/0.2^(-4) = [#permalink]

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New post 10 Sep 2017, 19:05
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Bunuel wrote:
\(\frac{0.8^{(-5)}}{0.2^{(-4)}} =\)

A. 5/1024

B. 5/64

C. 5/16

D. 25/16

E. 5/2

Exponent rules method

\(\frac{0.8^{(-5)}}{0.2^{(-4)}} =\)

\(\frac{0.2^{(4)}}{0.8^{(5)}} =\)

\(\frac{(\frac{1}{5})^{4}}{(\frac{4}{5})^{5}} =\)


\(\frac{(\frac{1}{5})^{4}}{(\frac{4}{5})^{4}(\frac{4}{5})^{1}} =\)


\((\frac{1}{5})^4 * (\frac{5}{4})^4 * (\frac{5}{4})^1 =\)


\((\frac{1}{5} * \frac{5}{4})^4 *\frac{5}{4} =\)

\((\frac{1}{4^{4}})\) * \((\frac{5}{4}) =\)


\((\frac{5}{4^{5}})\) =

\(\frac{5}{1024}\)

ANSWER A

Multiply fractions method (I used this method, and it was pretty quick, but decided that exponent rules above might be easier)

\(\frac{(\frac{2}{10})^{4}}{(\frac{8}{10})^{5}}\) =

\(\frac{\frac{2}{10}}{\frac{8}{10}}\) * \(\frac{\frac{2}{10}}{\frac{8}{10}}\) * \(\frac{\frac{2}{10}}{\frac{8}{10}}\) * \(\frac{\frac{2}{10}}{\frac{8}{10}}\) * \(\frac{1}{\frac{8}{10}}\)

There are five terms in the expression immediately above. Simplify one of the first four terms (simplified result gets multiplied four times):

\(\frac{\frac{2}{10}}{\frac{8}{10}}\) ====> \(\frac{2}{10} * \frac{10}{8} = \frac{1}{4}\) (four of these get multiplied)

Simplify the fifth (and last) term: Dividing by \(\frac{8}{10}\) = dividing by \(\frac{4}{5}\) = multiplying by \(\frac{5}{4}\), so final expression to calculate is

\(\frac{1}{4} * \frac{1}{4} * \frac{1}{4} * \frac{1}{4} * \frac{5}{4}\) =

\(\frac{5}{4^{5}}\) =

5/1024

ANSWER A

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Intern
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Kudos [?]: 4 [0], given: 18

Re: 0.8^(-5)/0.2^(-4) = [#permalink]

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New post 11 Sep 2017, 09:07
Bunuel wrote:
\(\frac{0.8^{(-5)}}{0.2^{(-4)}} =\)

A. 5/1024

B. 5/64

C. 5/16

D. 25/16

E. 5/2


The above can be reduced to (8*10^-1)^-5/(2*10^-1)^-5

(8*10^-1)^-5 = (2^(3*-5))(10^(-1*-5)) = 10^5/2^15 --- 1

Likewise, (2*10^-1)^-5 = 10^4/2^4 --- 2

dividing 1 by 2 we get 10/2^11 , 10 can b written as 2 * 5 so the result would be 5/2^10 = 5/1024

Hence A.

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Re: 0.8^(-5)/0.2^(-4) = [#permalink]

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New post 14 Sep 2017, 10:42
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Bunuel wrote:
\(\frac{0.8^{(-5)}}{0.2^{(-4)}} =\)

A. 5/1024

B. 5/64

C. 5/16

D. 25/16

E. 5/2


We can simplify the given expression:

(8/10)^(-5)/(2/10)^(-4)

(4/5)^(-5)/(1/5)^(-4)

(5/4)^(5)/(5)^(4)

(5^5/4^5)/5^4

5/4^5

5/1024

Answer: A
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Kudos [?]: 829 [0], given: 5

Re: 0.8^(-5)/0.2^(-4) =   [#permalink] 14 Sep 2017, 10:42
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