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# M31-45

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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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20 Jun 2015, 10:40
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Difficulty:

45% (medium)

Question Stats:

63% (00:43) correct 37% (01:06) wrong based on 27 sessions

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What is the value of $$k$$?

(1) $$(-k)^5 = -k^5$$

(2) $$(-k)^4 = -k^4$$

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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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20 Jun 2015, 10:40
Official Solution:

What is the value of $$K$$?

(1) $$(-k)^5 = -k^5$$. This is the same as $$-k^5 = -k^5$$, which holds true for any value of $$k$$. Not sufficient.

(2) $$(-k)^4 = -k^4$$. Since $$(-k)^4 = k^4$$, then we have that $$k^4 = -k^4$$, which gives $$2k^4 = 0$$, or $$k = 0$$. Sufficient.

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Joined: 30 Jul 2017
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13 Dec 2017, 05:35
Hello,

Could you please explain the difference between (-k^3), (-k)^3, -(k)^3 and -(k^3) ? I have problems understanding this. Many thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52971

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13 Dec 2017, 06:03
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krikre wrote:
Hello,

Could you please explain the difference between (-k^3), (-k)^3, -(k)^3 and -(k^3) ? I have problems understanding this. Many thanks

For odd powers all of those are the same: -k^3.

For even powers: (-k)^2 = k^2 and -(k^2) = -k^2.
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13 Dec 2017, 06:46
Bunuel

Just to further elaborate though.. (-k^3) = -k * -k * -k, whereas -(k)^3 means -(k*k*k) right? (same result but the way to calculate it is different?) So the power has priority over the sign if the sign is not within the brackes along with k?

Kindly let me know if I understand this correctly.
Thank you.
Kristian

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Joined: 02 Sep 2009
Posts: 52971

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13 Dec 2017, 07:00
krikre wrote:
Bunuel

Just to further elaborate though.. (-k^3) = -k * -k * -k, whereas -(k)^3 means -(k*k*k) right? (same result but the way to calculate it is different?) So the power has priority over the sign if the sign is not within the brackes along with k?

Kindly let me know if I understand this correctly.
Thank you.
Kristian

_________________

No.

-k^3 = - (k*k*k).
(-k)^3 = (-k)(-k)(-k)
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Re: M31-45   [#permalink] 13 Dec 2017, 07:00
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# M31-45

Moderators: chetan2u, Bunuel

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