Final answer:
The expression 216^1/3 simplifies to 6, because taking the cubic root of 216, which is finding a number that when cubed equals 216, gives us 6 since 6 x 6 x 6 equals 216. This operation is part of algebraic concepts involving exponents and radicals.
Step-by-step explanation:
The student has asked to simplify the expression 216^1/3. To simplify this expression, we need to understand that 216 raised to the 1/3 (or cubic root) is the same as finding the number that, when multiplied by itself three times, equals 216. In mathematics, cubic roots fall under the category of radicals, which are operations inverse to exponents.
216 is actually a perfect cube, since 6 x 6 x 6 = 216. Therefore, the cubic root of 216 is 6. Hence, 216^1/3 simplifies to 6. In summary, when a number is raised to the power 1/3, we are looking for the cubic root of that number, which is a fundamental concept in algebra.
Simplifying expressions like these are common in algebra, and understanding how to manipulate exponents and roots is essential. When working with exponents, it's helpful to remember that the laws of exponents apply and can be used to simplify or modify expressions where necessary.