Before dividing the given radical expressions, we need to answer two questions.
- Can the expressions be divided?
- If so, do symbols need to be added to the answer?
The rule regarding dividing states that if
are real numbers and
Because we are assuming that both radicals are and we can see that the given expressions have the same index, we can
divide them. Now, to answer the second question, consider the rule regarding absolute value symbols.
Because our radicals have an odd
root, negative numbers will not cause the expressions to be . Therefore, we don't need to worry about absolute value symbols.
Next, let's simplify the radical expression by finding all of the perfect cubes inside the radical.
Let's stop here for a moment and consider the fact that we need to have a rationalized denominator. If we simplified all of the perfect cubes as they are, we would be left with
in the denominator. To avoid this, we can multiply the numerator and denominator by a factor that will create a perfect cube, which in this case is