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9^9-9^2

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9^9-9^2

by ska7945 » Mon Sep 08, 2008 5:38 pm
Which of the following is closest in value to 9^9 – 9^2 ?

A. 9^9
B. 9^8
C. 9^7
D. 9^6
E. 9^5
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by ska7945 » Mon Sep 08, 2008 5:39 pm
9^9-9^2=
9^2(9^7-1)

what do i do for next step?
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by just_do_it » Mon Sep 08, 2008 5:50 pm
(9^7 -1) is closest to 9^7
therefore expression in paranthesis ~ 9^7

9^7 * 9^2 = 9^9

hope this helps.
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by cramya » Mon Sep 08, 2008 6:32 pm
9^9 - 9^2

Like Just do it said Take 9^2 the common factor out

9^2 (9^7 - 1)


So 9^2 (9^7 - 1)

= 9^2 (9 ^ 7) (since 9 ^ 7 - 1 is very close to 9 ^ 7)
=9^2(9^7)
=9^9
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by cramya » Mon Sep 08, 2008 6:33 pm
The approximation works since the questions asks for the closet value.

9^7 - 1 would be closest to 9 ^ 7
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by Shrinidhi » Wed Sep 10, 2008 7:06 pm
I also did the same way as suggested by other members.
Another way to look at it is,

9^9 would result in such a huge number that 9^2, i.e. 81 would be insignificant. Hence, answer would be 9^9.

As I said, this struck me after I had solved. :roll:
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