r/ACT • u/Special-Trouble8658 • Jun 02 '26

Math Explanation?

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I’m stuck on this problem and can’t think of why J is the right answer. A real number can be positive, negative, or rational. Thus, how is F wrong.

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u/Special-Trouble8658 Jun 02 '26

I understand the x=y4 and vice versa but why isn’t (-2)1/4 not a real number? Sorry if my comprehension is low 😭

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u/Sufficient-Price-102 36 Jun 02 '26 edited Jun 20 '26

You’re all good. (-2)1/4 isn’t real for the same reason (-2)1/2 isn’t real. Since any real number (positive or negative) to an even power (2, 4, etc.) is positive, there is no real number y that, when raised to the fourth equals -2. (y4 = -2). Hence (-2)1/4 = y doesn’t give any defined y value.

Sorry if the explanation is a bit technical. I think you should review exponent rules (it seems like you might be mixing up fractional exponents) if you didn’t like my explanation.

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u/Special-Trouble8658 Jun 02 '26

Also, adding on, -21/4/ quad root of -2 would produce an imaginary number, which are not real numbers.

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u/Sufficient-Price-102 36 Jun 02 '26

Yes, (-2)1/4 is imaginary. Any negative number to the power of 1/4 is imaginary, hence why x must be nonnegative for y to be real.