Final answer:
The cube root of 125/216 is 5/6.
Step-by-step explanation:
To find the cube root of the fraction 125/216, we can take the cube root of both the numerator and the denominator separately.
We know that 5³ = 125 and 6³ = 216, therefore, the cube root of 125/216 is 5/6.
This result can also be expressed using the property of exponents which states that
(a/b)³ = a³/b³, so ∛(a/b) = ∛(a)/∛(b).
Thus, in this case,
∛(125/216) = ∛(125)/∛(216) = 5/6.
The use of the cube root function is a way to reverse the operation of raising a number to the power of three.
So as 5 raised to the power of three is 125, then the cube root of 125 is 5; and as 6 raised to the power of three is 216, the cube root of 216 is 6.
Combining these two we get 5/6 as our final answer.