Final answer:
The fifth root of a number is a value that, when multiplied by itself five times, gives the original number. It can also be expressed as raising a number to the 1/5th power. Calculators can find a fifth root by raising to the 0.2 power.
Step-by-step explanation:
The term "the fifth root of" refers to a mathematical operation used to find a number that, when multiplied by itself five times, equals the original number. To illustrate this concept, let's look at an integer raised to a power, for example, 4³ which means 4 × 4 × 4. Similarly, a fifth root can be expressed as a fractional exponent, such as x¹⁄₅ which is equivalent to the fifth root of x (√x). Employing this logic, if you were to take the fifth root of 32, which is 32¹⁄₅, you would get 2, because 2 raised to the power of 5 (2⁵) equals 32. Understanding how to perform these operations with different roots, such as cube roots or fourth roots, is essential in solving various mathematical problems, especially in cases involving equilibrium or exponential growth. A calculator can generally perform these operations by raising a number to the appropriate fractional power.