The correct answer is:
C) false; The number can be rewritten as a fraction with 1 in the numerator and the number raised to the positive power in the denominator. The denominator is greater than the numerator, so simplifying the fraction results in a number less than 1. For example, (1/10)−3 is written as 1/(10)³. This is then simplified to 1/1000.
Explanation:
When a number \( x \) is between 0 and 1 (e.g., \( x = \frac{1}{10} \)), raising it to a negative exponent means taking the reciprocal and raising the base \( x \) to the positive of that exponent.
For example, \( (1/10)^{-3} = (10/1)^{3} = 10^3 = 1000 \).
However, when you consider the relationship of raising numbers less than 1, the operation indeed results in a number greater than 1. Thus, we can clarify that the statement "If a number between 0 and 1 is raised to a negative power, the result is a number greater than 1" is indeed true, but option D is misleading about how the numbers are written.
The answer should be corrected to show that the initial statement is actually true despite the flawed explanation in the options. Therefore, the statement itself is true, with option D being the only correct answer textually but misleading in its reasoning.
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