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02 Jan 2005, 23:38
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Is (-a)^b negative?
(1) b is negative.
(2) b is even.
(1) b is negative.
(2) b is even.
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03 Jan 2005, 00:20
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A negative exponent turns a number into a fraction. 5 ^ -2 = 1 / 5 ^ 2 = 1 / 25. But the fact that a number is a fraction is unrelated to whether that number is positive or negative. So statement 1 alone is no help.
An even exponent, on the other hand, always yields a positive number or zero. This is because the base number will be multiplied by itself an even number of times and any minus signs will all cancel out. (-3)^4 = -3 * -3 * -3 * -3 = (-3 * -3) * (-3 * -3) = 9 * 9 = 81.
So statement 2 is enough to assure us that, no, the expression can not yield a negative. The answer is B.
An even exponent, on the other hand, always yields a positive number or zero. This is because the base number will be multiplied by itself an even number of times and any minus signs will all cancel out. (-3)^4 = -3 * -3 * -3 * -3 = (-3 * -3) * (-3 * -3) = 9 * 9 = 81.
So statement 2 is enough to assure us that, no, the expression can not yield a negative. The answer is B.
03 Jan 2005, 06:18
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Statement 1 the number is always negative though the number is a fraction or integer the Q does not ask that its always negative
Statement 2 the number is always positive
ANSWER is D
Statement 2 the number is always positive
ANSWER is D
