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

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Math Expert
Joined: 02 Sep 2009
Posts: 46128

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10 Sep 2017, 05:33
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Difficulty:

15% (low)

Question Stats:

76% (01:36) correct 24% (01:46) wrong based on 51 sessions

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

A. 5/1024

B. 5/64

C. 5/16

D. 25/16

E. 5/2

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Joined: 26 Feb 2016
Posts: 2800
Location: India
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10 Sep 2017, 06:42
1
$$\frac{0.8^{(-5)}}{0.2^{(-4)}} = \frac{0.2^{(4)}}{0.8^{(5)}} = \frac{0.2*0.2*0.2*0.2}{0.8*0.8*0.8*0.8*0.8} = \frac{1}{4*4*4*4*0.8} = \frac{10}{4*4*4*4*4*2} = \frac{5}{4^5} = \frac{5}{1024}$$(Option A)
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Joined: 22 May 2016
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10 Sep 2017, 19:05
1
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

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

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

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

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

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

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

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

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

$$\frac{5}{1024}$$

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

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Joined: 21 Nov 2016
Posts: 45

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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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Joined: 04 Mar 2011
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14 Sep 2017, 10:42
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

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