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

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Senior Manager
Joined: 29 Oct 2019
Posts: 314

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25 Feb 2020, 23:33
1
1
00:00

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/
Manager
Joined: 22 Sep 2014
Posts: 157
Location: United States (CA)

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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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CrackVerbal Representative
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 1817
Location: India
GMAT 1: 780 Q51 V46

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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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Senior Manager
Joined: 29 Oct 2019
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21 Mar 2020, 08:30
What are the other ways to resolve the problem above?
Re: (0.6)^(-8)(0.5)^(-4)/((0.3)^(-6)(0.12)^(-2)) =   [#permalink] 21 Mar 2020, 08:30