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If (1/2)^N >-8, which of the following could be the value of
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29 Sep 2020, 22:08
29 Sep 2020, 22:08
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Question Stats:
41% (00:59) correct
58% (00:48) wrong based on 24 sessions
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If \((-\frac{1}{2})^N >-8\), which of the following could be the value of \(N\)?
Indicate all that apply
A -10
B -7
C -3
D 0
E 3
F 10
Indicate all that apply
A -10
B -7
C -3
D 0
E 3
F 10
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Official Answer
A,D,E,F
Re: If (1/2)^N >-8, which of the following could be the value of
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01 Oct 2020, 02:07
01 Oct 2020, 02:07
1
For (-1/2)^N > -8 then the RHS expression must be positive or small negative
So trying each number
We have -10, 0
Posted from my mobile device
So trying each number
We have -10, 0
Posted from my mobile device
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Re: If (1/2)^N >-8, which of the following could be the value of
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01 Oct 2020, 06:18
01 Oct 2020, 06:18
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Sunsha wrote:
If \((-\frac{1}{2})^N >-8\), which of the following could be the value of \(N\)?
Indicate all that apply
A -10
B -7
C -3
D 0
E 3
F 10
Indicate all that apply
A -10
B -7
C -3
D 0
E 3
F 10
Two important rules:
ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE
An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE
Since \((-\frac{1}{2})^N \) will be positive for all EVEN values of N, we can see that N = -10, 0 and 10, will yield powers that are greater than -8
So, answer choices A, D and F work so far.
Let's just test the remaining answer choices...
B) -7
Useful rule: \((\frac{a}{b})^{-k} = (\frac{b}{a})^{k}\)
So, \((-\frac{1}{2})^{-7} = (-\frac{2}{1})^{7}=(-2)^{7}=-128\)
Since \(-128 < -8\), answer choice B isn't a solution.
C) -3
\((-\frac{1}{2})^{-3} = (-\frac{2}{1})^{3}=(-2)^{3}=-8\)
Since \(-8 = -8\), answer choice C isn't a solution.
E) 3
\((-\frac{1}{2})^{3} = -\frac{1}{8}\)
Since \(-\frac{1}{8} > -8\), answer choice E works.
Answer: A, D, E, F
