To simplify this expression using exponent properties, we need to rewrite the numbers with the same base.
3√216 can be written as (216)^(1/3).
27^1/3 can be written as (3^3)^(1/3).
Using the exponent rule (a^m)^n = a^mn, we can simplify (3^3)^(1/3) to 3^(3*(1/3)), which becomes 3^1, which is equal to 3.
Now, we can rewrite the expression as (216)^(1/3) / 3.
We can rewrite 216 as 6^3, so the expression becomes (6^3)^(1/3) / 3.
Using the exponent rule (a^m)^n = a^mn, we can simplify (6^3)^(1/3) to 6^(3*(1/3)), which becomes 6^1, which is equal to 6.
Now, the expression becomes 6 / 3, which simplifies to 2.
Therefore, option 3. 2 is the correct answer.
Which of the following expressions is equivalent to 3√216/27^1/3 when applying the exponent properties?(1 point)
Options
1. 8
2. 1/2
3. 2
4. 18
1 answer