Explanation:
To rationalize the denominator of the expression 3/∜(2³), you want to eliminate the fourth root (∜).
First, express 2³ as 8 because 2³ = 8.
So, you have 3/∜8.
To eliminate the fourth root (∜), you can rewrite it as a fractional exponent with a denominator of 4:
3/∜8 = 3/(8^(1/4))
Now, you can use the rule that states a^(1/n) = √(a^(1/n))^n to simplify the expression:
3/(8^(1/4)) = 3/(√(8^1)) = 3/(√8)
To further simplify, you can rationalize the denominator by multiplying both the numerator and denominator by √8:
(3/(√8)) * (√8/√8) = (3√8)/8
So, the rationalized form of 3/∜(2³) is (3√8)/8.