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# What is the value of (−8)^(−3)?

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Math Expert
Joined: 02 Sep 2009
Posts: 58339
What is the value of (−8)^(−3)?  [#permalink]

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06 Mar 2019, 23:56
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Difficulty:

5% (low)

Question Stats:

95% (00:28) correct 5% (00:17) wrong based on 21 sessions

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What is the value of $$(− 8)^{−3}$$?

A. $$− 512$$

B. $$− 24$$

C. $$− 2$$

D. $$- \frac{1}{2}$$

E. $$- \frac{1}{512}$$

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Joined: 02 Aug 2009
Posts: 7958
Re: What is the value of (−8)^(−3)?  [#permalink]

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07 Mar 2019, 00:27
Bunuel wrote:
What is the value of $$(− 8)^{−3}$$?

A. $$− 512$$

B. $$− 24$$

C. $$− 2$$

D. $$- \frac{1}{2}$$

E. $$- \frac{1}{512}$$

A NEGATIVE exponent, -3 here, or power can be made positive by taking RECIPROCAL of the base, -8 here.
Therefore, $$(− 8)^{−3}=\frac{1}{(-8)^3}=\frac{1}{(-8)(-8)(-8)}$$

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Re: What is the value of (−8)^(−3)?  [#permalink]

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07 Mar 2019, 00:57
Bunuel wrote:
What is the value of $$(− 8)^{−3}$$?

A. $$− 512$$

B. $$− 24$$

C. $$− 2$$

D. $$- \frac{1}{2}$$

E. $$- \frac{1}{512}$$

$$(− 8)^{−3}=\frac{1}{(-8)^3}=\frac{1}{(-512)}$$
thus, E, $$- \frac{1}{512}$$ is the correct answer
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Re: What is the value of (−8)^(−3)?  [#permalink]

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07 Mar 2019, 02:21
Bunuel wrote:
What is the value of $$(− 8)^{−3}$$?

A. $$− 512$$

B. $$− 24$$

C. $$− 2$$

D. $$- \frac{1}{2}$$

E. $$- \frac{1}{512}$$

$$(− 8)^{−3}$$

-1/8^3
-1/512
IMO E
Re: What is the value of (−8)^(−3)?   [#permalink] 07 Mar 2019, 02:21
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