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# 0.4^(-5)/0.2^(-4) =

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Math Expert
Joined: 02 Sep 2009
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07 Sep 2017, 23:26
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Difficulty:

25% (medium)

Question Stats:

82% (01:41) correct 18% (01:50) wrong based on 94 sessions

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$$\frac{0.4^{(-5)}}{0.2^{(-4)}} =$$

A. 5

B. 2

C. 1/2

D. 5/16

E. 5/32

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Re: 0.4^(-5)/0.2^(-4) =  [#permalink]

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07 Sep 2017, 23:56
$$\frac{0.4^{(-5)}}{0.2^{(-4)}}$$ = $$\frac{0.2^{(4)}}{0.4^{(5)}}$$ = $$\frac{0.2*0.2*0.2*0.2}{0.4*0.4*0.4*0.4*0.4}$$ = $$\frac{10}{2*2*2*2*4}$$ = $$\frac{5}{2*2*2*2*2}$$ = $$\frac{5}{32}$$(Option E)
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Re: 0.4^(-5)/0.2^(-4) =  [#permalink]

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08 Sep 2017, 02:39
$$\frac{0.4^(-5)}{0.2^(-4)} = \frac{0.2^4}{0.4^5}$$

= $$(2/10)^4 / (4/10)^5$$

= $$\frac{2^4 * 10^ 5}{4^5 * 10^4} =\frac{2^4 * 10^ 5}{2^(10) * 10^4} =\frac{10}{2^5} =\frac{5}{32}$$

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Re: 0.4^(-5)/0.2^(-4) =  [#permalink]

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08 Sep 2017, 05:14
$$0.4 ^(-5) / 0.2 ^(-4) = 0.2^4 / 2^5 * 0.2^5 = 1/(32 * 0.2) = 10/64 = 5/32$$

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Re: 0.4^(-5)/0.2^(-4) =  [#permalink]

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11 Sep 2017, 15:57
Bunuel wrote:
$$\frac{0.4^{(-5)}}{0.2^{(-4)}} =$$

A. 5

B. 2

C. 1/2

D. 5/16

E. 5/32

First, we convert the decimal values to fractions and then we simplify the given expression:

[(2/5)^-5]/[(1/5)^-4]

[(5/2)^5]/[(5)^4]

(5^5/2^5)/(5^4)

5/2^5

5/32

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Re: 0.4^(-5)/0.2^(-4) =  [#permalink]

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14 Oct 2018, 23:52
0.4^(-5)/0.2^(-4) = (0,2*2)^(-5) / 0.2^(-4) = 0,2^(-5)*2^(-5) / 0.2^(-4) = 0.2^(-1) * 2^(-5) = 10/2 * 1/32 = 5/32
Re: 0.4^(-5)/0.2^(-4) =   [#permalink] 14 Oct 2018, 23:52
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# 0.4^(-5)/0.2^(-4) =

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