Final answer:
The cube root of -64, written as \(\sqrt[3]{-64}\), is -4. This is found by identifying the number that when cubed gives -64, which is -4 since \((-4) \times (-4) \times (-4) = -64\).
Step-by-step explanation:
The student is asking to evaluate the cube root of -64, which is written as \(\sqrt[3]{-64}\). Cube roots are a type of radical expression where you are looking for a number that when multiplied by itself three times gives the original number. In this case, since the cube root of 64 is 4 (because \(4 \times 4 \times 4 = 64\)), and given that we are looking for the cube root of -64, we need the negative cube root, which is -4.
This is because \((-4) \times (-4) \times (-4) = -64\). Therefore, \(\sqrt[3]{-64} = -4\). This concept is closely related to the properties of exponents and powers, where a negative base raised to an odd exponent remains negative.