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10 Sep 2017, 05:33
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (02:03) correct
21%
(02:06)
wrong
based on 87
sessions
History
Date
Time
Result
Not Attempted Yet
\(\frac{0.8^{(-5)}}{0.2^{(-4)}} =\)
A. 5/1024
B. 5/64
C. 5/16
D. 25/16
E. 5/2
A. 5/1024
B. 5/64
C. 5/16
D. 25/16
E. 5/2
10 Sep 2017, 06:42
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\(\frac{0.8^{(-5)}}{0.2^{(-4)}} = \frac{0.2^{(4)}}{0.8^{(5)}} = \frac{0.2*0.2*0.2*0.2}{0.8*0.8*0.8*0.8*0.8} = \frac{1}{4*4*4*4*0.8} = \frac{10}{4*4*4*4*4*2} = \frac{5}{4^5} = \frac{5}{1024}\)(Option A)
10 Sep 2017, 19:05
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Bunuel
Exponent rules method
\(\frac{0.8^{(-5)}}{0.2^{(-4)}} =\)
\(\frac{0.2^{(4)}}{0.8^{(5)}} =\)
\(\frac{(\frac{1}{5})^{4}}{(\frac{4}{5})^{5}} =\)
\(\frac{(\frac{1}{5})^{4}}{(\frac{4}{5})^{4}(\frac{4}{5})^{1}} =\)
\((\frac{1}{5})^4 * (\frac{5}{4})^4 * (\frac{5}{4})^1 =\)
\((\frac{1}{5} * \frac{5}{4})^4 *\frac{5}{4} =\)
\((\frac{1}{4^{4}})\) * \((\frac{5}{4}) =\)
\((\frac{5}{4^{5}})\) =
\(\frac{5}{1024}\)
ANSWER A
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
ANSWER A
