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In the math theory, we know have $$(x)^{\frac{m}{n}=}\sqrt[n]{x^m} \ ,$$ it means $$(-1.5)^{\frac{1}{0.3}}=(-1.5)^{\frac{10}{3}}=\sqrt[3]{(-1.5)^{10}}=\sqrt[3]{1.5^{10}}\simeq 3.8634 \ .$$ But in mathematica, when we input (-1.5)^(1/0.3) we will get a complex number, i.e. -1.93170528-3.3458117i Why the result is different? Which is right?

J. M.'s missing motivation
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    Both. In fact, it's a matter of choice which of the three complex cubic roots to return as a result. You chose the real one, Mathematica chose differently. Take a look at the result of Solve[(-1.5)^(10) == x^3, x]. – MarcoB Sep 30 '18 at 01:59
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    Look up the concept of "principal value" and the Mathematica function Surd[]. – J. M.'s missing motivation Sep 30 '18 at 02:08

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