To determine the simplified form of [tex]\( -64^{\frac{1}{3}} \)[/tex], we'll follow the process of finding the cube root of -64.
1. First, recall that the expression [tex]\( -64^{\frac{1}{3}} \)[/tex] represents the cube root of -64.
2. When we find the cube root of a negative number, we'll typically get a complex number as a result. This is because taking the root of a negative number without defining a domain for the root operation involves complex numbers.
Given the result [tex]\( (2+3.464101615137754j) \)[/tex], we can simplify this into a more recognizable form:
The cube root of -64 is:
[tex]\[ 2 + 3.464101615137754i \][/tex]
So, the simplified form of [tex]\( -64^{\frac{1}{3}} \)[/tex] is:
[tex]\[ \boxed{(2+3.464101615137754i)} \][/tex]
