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(6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) =

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tonebeeze
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(6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) = [#permalink] New post   Updated on: 24 Jan 2022, 08:47
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\(\frac{6.804^6*1.701^{-13}}{2^{19}*3.402^{-7}}\).

A. 0.8502
B. 1.000
C. 1.7010
D. 3.402
E. 6.804
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B

Originally posted by tonebeeze on 06 Oct 2010, 11:05.
Last edited by Bunuel on 24 Jan 2022, 08:47, edited 2 times in total.
Edited the question.
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Re: (6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) = [#permalink] New post   11 Mar 2012, 02:45
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the hardest thing here is to discern that:

2*1.701=3.402
4*1.701=6.804

In order to save time and avoid making mistakes by re-writing decimals, 3.402 can be substituted with '2x' and 6.804 with 4x. Therefore, the initial formula is quite simplified:

\(\frac{(4x)^6*x^-13}{2^19*(2x)^-7}\)

Afterwards, it takes 20 seconds to arrive to the final result
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(6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) = [#permalink] New post   06 Oct 2010, 11:18
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\(\frac{6.804^6*1.701^{-13}}{2^{19}*3.402^{-7}}=\)?

A. 0.8502
B. 1.000
C. 1.7010
D. 3.402
E. 6.804

\(\frac{6.804^6*1.701^{-13}}{2^{19}*3.402^{-7}}=\frac{(2^2*1.701)^6}{2^{19}*(2*1.701)^{-7}*1.701^{13}}=\frac{2^{12}*1.701^6*(2*1.701)^{7}}{2^{19}*1.701^{13}}=\frac{2^{12}*1.701^6*2^7*1.701^{7}}{2^{19}*1.701^{13}}=\frac{2^{19}*1.701^{13}}{2^{19}*1.701^{13}}=1\).

Answer: B.
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Re: (6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) = [#permalink] New post   26 Oct 2013, 13:03
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I realized something when looking at this one: they would never have you doing the kind of calculations that would lead to those long decimals. I figured it had to be B based simply on the fact that they rarely if ever have you calculating out that far past the decimal point.
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Re: (6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) = [#permalink] New post   06 Oct 2010, 11:21
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tonebeeze wrote:
Can you please walk me through simplifying this exponents problem. Thanks

(6.806)^6 (1.701)^-13
_________________________ =

(2)^9 (3.402)^-7


a. .8502
b. 1.000
b. 1.7010
c. 3.402
d. 6.804


I'm sure the question must have \((6.804)^6\) in the numerator; otherwise you won't have much simplification. I also suspect that the denominator should have a 2^19 in it, instead of 2^9; otherwise you won't get one of the five answer choices. With those changes, then if you notice that 3.402 = 2(1.701), and that 6.804 = (2^2)(1.701), we can factor out 2's in order to cancel:

\(\frac{(6.804)^6 (1.701)^{-13}}{(2^{19})(3.402)^{-7}} = \frac{(2^2)^6(1.701)^6 (1.701)^{-13}}{(2^{19})(2^{-7})(1.701)^{-7}} = \frac{(2^{12})(1.701)^{-7}}{(2^{12})(1.701)^{-7}} = 1\)
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Re: (6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) = [#permalink] New post   26 Feb 2014, 02:37
Re-writing the equation in the powers of 1.701 & 2 :

2^12 . 1.701^6 . 1.701^ -13

Divide by

2^19 . 2^ -7 . 1.701^-7

Answer = 1 = B
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Re: (6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) = [#permalink] New post   04 Mar 2024, 20:32
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Re: (6.804)^6*(1.701)^-13/(2)^19*(3.402)^(-7) = [#permalink]
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