Which of the following expressions is equivalent to 3√216/27^1/3 when applying the
exponent properties?(1 point)
Responses
1. 18
2. 1/2
3. 8
4. 2
The expression 3√216 can be simplified as the cube root of 216.
The cube root of 216 is 6, because 6 * 6 * 6 = 216.
Therefore, the expression 3√216 simplifies to 6.
27^1/3 is the cube root of 27, which is 3, because 3 * 3 * 3 = 27.
So the expression 3√216/27^1/3 simplifies to 6/3, which is 2.
Hence, the answer is option 4.
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.