Question
Evaluate the following. Click on "Not a real number" if applicable. (a) \( (-625)^{\frac{1}{4}}=\square \) (b) \( \quad(-216)^{\frac{1}{3}}=\square \)
Ask by Tyler Love. in the United States
Jan 24,2025
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Answer
(a) \( (-625)^{\frac{1}{4}} = \frac{5\sqrt{2}}{2} + \frac{5\sqrt{2}}{2}i \)
(b) \( (-216)^{\frac{1}{3}} = -6 \)
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Beyond the Answer
To evaluate the expressions: (a) The fourth root of \(-625\) is not a real number because we cannot raise a negative number to an even root and get a real number. Thus, \( (-625)^{\frac{1}{4}} = \text{Not a real number} \). (b) The cube root of \(-216\) is \(-6\) since \((-6)^3 = -216\). Therefore, \( (-216)^{\frac{1}{3}} = -6 \).