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(0.6)^(-8)(0.5)^(-4)/((0.3)^(-6)(0.12)^(-2)) =

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Senior Manager
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(0.6)^(-8)(0.5)^(-4)/((0.3)^(-6)(0.12)^(-2)) =  [#permalink]

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New post 25 Feb 2020, 23:33
1
1
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

52% (02:33) correct 48% (02:30) wrong based on 25 sessions

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\(\frac{(0.6)^{-8} (0.5)^{-4}}{(0.3)^{-6}(0.12)^{-2}} =\)

(A) 1/200

(B) 1/100

(C) 1/50

(d) 1/25

(E) 1/5

Source: https://gmatquantum.com/
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Re: [m][fraction](0.6)^{-8} (0.5)^{-4}/(0.3)^{-6}(0.12)^{-2}[/fraction][/m  [#permalink]

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New post 25 Feb 2020, 23:55
A=0.6^-4 * 0.6^-4 * 0.5^-4= 0.36^-2 * 0.3^-4

B=0.3^-4 * 0.3^-2 * 0.12^-2 = 0.036^-2 * 0.3^-4

A/B= 0.036^2 / 0.36^2 = 1/100

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Re: [m][fraction](0.6)^{-8} (0.5)^{-4}/(0.3)^{-6}(0.12)^{-2}[/fraction][/m  [#permalink]

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New post 26 Feb 2020, 00:11
1
This question can be solved very quickly if you can convert the decimals to their equivalent fractions. This is a skill that will also help you when you deal with questions on percentages. Therefore, try to make a table of common fractions and their percentage counterparts and use the table whenever you are solving a question like the above.

We also need to know some basic rules of exponents to get rid of the negative powers.
\(a^{-n}\) = \(\frac{1}{a^n}\)

0.6 = \(\frac{3}{5}\), 0.3 = \(\frac{3}{10}\), 0.12 = \(\frac{3}{25}\) and 0.5 = ½.

Substituting the above values in place of the decimals and using the exponent rule, the given expression can be rewritten as,

\((\frac{3}{25})^2\) * \((\frac{3}{10})^6\) / \((\frac{3}{5})^8\) * \((\frac{1}{2})^4\) which can be simplified as,

\((\frac{3^2}{5^4}) * (\frac{3^6 }{ 2^6*5^6}) / (\frac{3^8 }{5^8}) * \frac{1 }{ 2^4}\).

Simplifying the above by cancelling the respective powers, the expression simplifies to \(\frac{1 }{ 2^2 * 5^2}\) or \(\frac{1}{100}\).
The correct answer option is B.

Hope that helps!
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Re: (0.6)^(-8)(0.5)^(-4)/((0.3)^(-6)(0.12)^(-2)) =  [#permalink]

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New post 21 Mar 2020, 08:30
What are the other ways to resolve the problem above?
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Re: (0.6)^(-8)(0.5)^(-4)/((0.3)^(-6)(0.12)^(-2)) =   [#permalink] 21 Mar 2020, 08:30

(0.6)^(-8)(0.5)^(-4)/((0.3)^(-6)(0.12)^(-2)) =

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