Explain rational exponents as extensions of integer exponent rules and as radical notation.
Decide whether a negative number raised to a rational exponent is real
Problem
Is \((-8)^{1/3}\) a real number?
Big Picture
What this problem is really about
For a negative base, the reduced exponent denominator determines whether the corresponding real root exists. We’ll keep the parentheses around the base, identify the odd root index, rewrite the power as a radical, test the signed root by raising it back, and classify the result’s number system.
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