(a)

To solve for , you want to find the cube root of -125. The cube root function can handle negative numbers, so you have . As the cube root of 125 is 5, it follows that .

So, your answer is .

Now, have you ever wondered how ancient civilizations dealt with negative numbers? They often avoided them entirely until mathematicians in the Middle Ages started to normalize their usage, making calculations much more robust!

Next, if you ever find yourself struggling with cube roots, remember it can help to break down the number into its prime factors! For example, remember that 125 is (or ). Recognizing patterns and factors can alleviate errors in your calculations!