Exponent problem
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
cramya
- Legendary Member
- Posts: 2467
- Joined: Thu Aug 28, 2008 6:14 pm
- Thanked: 331 times
- Followed by:11 members
( (2y^3) ^ - 2/ (4x ^ - 5 ) ) ^ - 2
I have hghlighted the minus signs just to make sure the problem reads as is. Can u please confirm(sorry to bother again
)?
I am getting y ^ 12 / 256 x ^ 10 since the numerator and denominator reciprocates once inside the parenetheses due to negative exponents -2 and -5 and then again reciporocates due to the -2 outside.
I must be missing something here.... Will keep trying
I have hghlighted the minus signs just to make sure the problem reads as is. Can u please confirm(sorry to bother again
)?I am getting y ^ 12 / 256 x ^ 10 since the numerator and denominator reciprocates once inside the parenetheses due to negative exponents -2 and -5 and then again reciporocates due to the -2 outside.
I must be missing something here.... Will keep trying
-
iamcste
- Legendary Member
- Posts: 940
- Joined: Tue Aug 26, 2008 3:22 am
- Thanked: 55 times
- Followed by:1 members
Here we go !jnellaz wrote:I was careful to replicate this problem. Please let me know if you have any questions.
((2y^3)^-2/(4x^-5))^-2 =
[spoiler]Answer: 256y^12/x^10
[/spoiler][spoiler]
[/spoiler]
Answer and question both are perfect
((2y^3)^-2/(4x^-5))^-2
=( (2^-2*y^-6)/(4x^-5))^-2 ...aplying inner powers..(ab)^m=a^m*b^m
=(( 2^4*y^12)/( 4^-2*x^10)...applying external power..outer brackets..(ab)^m=a^m*b^m
=( ( 2^4* 4^2*y^12) / (x^10)..taking 4^-2 up
=(4^2* 4^2) * (y^12/x^10)....2 ^ 4= 4^2
=( 4 ^4) * (y^12/x^10)
=(256* y^12)/ x^10
-
iamcste
- Legendary Member
- Posts: 940
- Joined: Tue Aug 26, 2008 3:22 am
- Thanked: 55 times
- Followed by:1 members
4meonly wrote:I still do not understand how u got
fromiamcste wrote:=( 2^4*y^12)
Can somebody clarify?iamcste wrote:=(2^-2*y^-6)
(2^-2*y^-6) ^-2
Pls note outside the outer brackets there is a power of -2
Just apply that
(a*b)^m=a^m*b^m
a=2^-2 and m=-2
a^m=(2^-2)^-2
Now apply (a^m)^n=a^mn
mn=-2*-2=4 and a =2
hence a^mn=2^4
similary (y^-6)^-2
=y^12
hence
(2^-2*y^-6) ^-2=( 2^4*y^12)
-
4meonly
- Legendary Member
- Posts: 891
- Joined: Sat Aug 16, 2008 4:21 am
- Thanked: 27 times
- Followed by:1 members
- GMAT Score:660(
OK, agree with calculations, but I do not agree with logic.
you made -2 power of numerator. But why you haven't done it with denumerator?
(ab)/cd = (ab)^2 / cd
but it should be
(ab)/cd = (ab)^2 / (cd)^2
Am I missing something?
you made -2 power of numerator. But why you haven't done it with denumerator?
According to your logiciamcste wrote: =( (2^-2*y^-6)/(4x^-5))^-2 ...aplying inner powers..(ab)^m=a^m*b^m
=(( 2^4*y^12)/( 4^-2*x^10)...applying external power..outer brackets..(ab)^m=a^m*b^m
(ab)/cd = (ab)^2 / cd
but it should be
(ab)/cd = (ab)^2 / (cd)^2
Am I missing something?
-
parallel_chase
- Legendary Member
- Posts: 1153
- Joined: Wed Jun 20, 2007 6:21 am
- Thanked: 146 times
- Followed by:2 members
Here is a long way of doing this problem, simply for better understanding.
[(2y^3)^-2/(4x^-5)]^-2
Switch the numerator and denominator -power becomes positive
[ (4x^-5) / 2y^3)^-2 ]^2
expand and let it blow 8)
(4^2 * x^-10) / [(2^-2)^2 (y^-6)^2]
=> (4^2 * x^-10) / [(2^-4 (y^-12)]
switch negative powers to numerator and denominator so it becomes positive
(4^2 * 2^4 * y^12) / x^10
256 * y^12 / x^10
Hope this helps.
[(2y^3)^-2/(4x^-5)]^-2
Switch the numerator and denominator -power becomes positive
[ (4x^-5) / 2y^3)^-2 ]^2
expand and let it blow 8)
(4^2 * x^-10) / [(2^-2)^2 (y^-6)^2]
=> (4^2 * x^-10) / [(2^-4 (y^-12)]
switch negative powers to numerator and denominator so it becomes positive
(4^2 * 2^4 * y^12) / x^10
256 * y^12 / x^10
Hope this helps.
No rest for the Wicked....
