Answer: 1/5
Step-by-step explanation: To simplify [tex]125^{-1/3}[/tex], let's first deal with the negative in the exponent. [tex]125^{-1/3}[/tex] means the same thing as [tex]\frac{1}{125^1/3}[/tex].
Now, it's important to understand that if we have an exponent of 1/3, we take the cube root of the base. In other words, [tex]125^{1/3}[/tex] means the same thing as the cube root of 125. So we have [tex]\frac{1}{\sqrt[3]{125}}[/tex].
Next, it's important to recognize that 125 is a perfect cube (5 x 5 x 5) or 5³. So the cube root of 125 is 5 and we have 1/5.
Therefore, [tex]125^{-1/3}[/tex] simplifies to 1/5.
Make sure you know your perfect cubes such as 125. It will make life much easier as you work through these types of problems.
