To simplify the expression 3√216/27^(1/3) using the exponent properties, we can rewrite the numbers under the root and the exponent in their prime factorization form:
3√(2^3 * 3^3)/(3^1/3)
Now, let's simplify further:
3√[(2^3 * 3^3)/(3^1/3)]
Using the exponent property, we can simplify the expression inside the root:
3√[(2^3 * 3^3)/(3^(1/3 * 3))]
Since the exponent 1/3 is the same as cube root, we have:
3√[(2^3 * 3^3)/(3^1)]
Now, let's simplify the expression inside the root:
3√[(8 * 27)/3]
After simplifying the expression inside the root, we get:
3√[216/3]
Finally, we can simplify the expression under the root:
3√72
The cube root of 72 is 4, so the final answer is:
4
Therefore, the equivalent expression is 4.
Hence, the correct answer is 4.