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19 Feb 2013, 23:52
Kudos
Bookmarks
Hi
Sorry , I don't know how to format it correctly here, so pasting the image.
My doubt is .. If we take 5 raised to 4 as common in the denominator,
we will be left with
[5 raised to 4 ( 5 raised to 3 - 1 ) ] raised to -2.
Now this can be deduced to
5 raised to 2 * [5 raised to 3 - 1 ] raised to -2 ..
So 25 remains in the denominator .
However , if we do not take 5 raised to 4 as common in the denominator, the entire denominator can be taken above in the numerator by changing the sign of the exponent to positive 2.
In this case no 25 remains in the denominator.
I don't understand where I am going wrong . Kindly help.
Sorry , I don't know how to format it correctly here, so pasting the image.
My doubt is .. If we take 5 raised to 4 as common in the denominator,
we will be left with
[5 raised to 4 ( 5 raised to 3 - 1 ) ] raised to -2.
Now this can be deduced to
5 raised to 2 * [5 raised to 3 - 1 ] raised to -2 ..
So 25 remains in the denominator .
However , if we do not take 5 raised to 4 as common in the denominator, the entire denominator can be taken above in the numerator by changing the sign of the exponent to positive 2.
In this case no 25 remains in the denominator.
I don't understand where I am going wrong . Kindly help.
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21 Feb 2013, 11:06
Kudos
Bookmarks
There is no denominator to worry about, move the denominator to the numerator and change the sign to positive.
(3^5 - 3^2)^2 * (5^7 - 5^4)^2
Then factor
(3^2(3^3 - 1))^2 * (5^4(5^3 - 1))^2
Simplify
(9*26)^2 * (625*124)^2
E is the answer because there are only 2 factors of 13 in the above expression and E has 4.
(3^5 - 3^2)^2 * (5^7 - 5^4)^2
Then factor
(3^2(3^3 - 1))^2 * (5^4(5^3 - 1))^2
Simplify
(9*26)^2 * (625*124)^2
E is the answer because there are only 2 factors of 13 in the above expression and E has 4.
22 Feb 2013, 01:54
Kudos
Bookmarks
OE is below:
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 analyze each option you'll see 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 analyze each option you'll see 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.
