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16 Sep 2014, 01:25
Kudos
Bookmarks
If \(y=\frac{(3^5-3^2)^2}{(5^7-5^4)^{-2} }\), then \(y\) is NOT divisible by which of the following?
A. \(6^4\)
B. \(62^2\)
C. \(65^2\)
D. \(15^4\)
E. \(52^4\)
A. \(6^4\)
B. \(62^2\)
C. \(65^2\)
D. \(15^4\)
E. \(52^4\)
21 Jul 2015, 05:43
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lucassandrade
Consider this: \((ab-ac)^2=(a(b-c))^2=a^2*(b-c)^2\), so \((3^5-3^2)^2=(3^2*(3^3-1))^2=(3^2)^2*(3^3-1)^2=3^4*(3^3-1)^2\).
The same for (5^7-5^4)^2
Hope it helps.
16 Sep 2014, 01:25
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Official Solution:
If \(y=\frac{(3^5-3^2)^2}{(5^7-5^4)^{-2} }\), then \(y\) is NOT divisible by which of the following?
A. \(6^4\)
B. \(62^2\)
C. \(65^2\)
D. \(15^4\)
E. \(52^4\)
\(y=\frac{(3^5-3^2)^2}{(5^7-5^4)^{-2} }=\)
\(=(3^5-3^2)^2*(5^7-5^4)^2=\)
\(=3^4*(3^3-1)^2*5^8*(5^3-1)^2=\)
\(=3^4*26^2*5^8*124^2=\)
\(=2^6*3^4*5^8*13^2*31^2\).
Now, if you examine each option, it becomes clear that only \(52^4=2^8*13^4\) is not a factor of \(y\), since the power of 13 in it is higher than the power of 13 in \(y\).
Answer: E
If \(y=\frac{(3^5-3^2)^2}{(5^7-5^4)^{-2} }\), then \(y\) is NOT divisible by which of the following?
A. \(6^4\)
B. \(62^2\)
C. \(65^2\)
D. \(15^4\)
E. \(52^4\)
\(y=\frac{(3^5-3^2)^2}{(5^7-5^4)^{-2} }=\)
\(=(3^5-3^2)^2*(5^7-5^4)^2=\)
\(=3^4*(3^3-1)^2*5^8*(5^3-1)^2=\)
\(=3^4*26^2*5^8*124^2=\)
\(=2^6*3^4*5^8*13^2*31^2\).
Now, if you examine each option, it becomes clear that only \(52^4=2^8*13^4\) is not a factor of \(y\), since the power of 13 in it is higher than the power of 13 in \(y\).
Answer: E
