Which expression is equivalent to 24 Superscript one-third?
2 StartRoot 3 EndRoot
2 RootIndex 3 StartRoot 3 EndRoot
2 StartRoot 6 EndRoot
2 RootIndex 3 StartRoot 6 EndRoot
24^(1/3) = 8^(1/3) * 3^(1/3) = 2 * 3^(1/3) = 2cbrt(3)
24 = 2^3 * 3, so ∛24 = 2∛3
The expression that is equivalent to 24 raised to the power of one-third is 2 StartRoot 3 EndRoot.
To determine which expression is equivalent to 24 raised to the power of one-third, we need to simplify each option and find the one that matches.
Option 1: 2 √3
This is equivalent to the square root of 3, so it is not the correct expression.
Option 2: 2 √₃√₃
This is equivalent to the cube root of 3, multiplied by another cube root of 3. The cube root of 3 × 3 is the same as the cube root of 9. Hence, this option simplifies to: 2 √₃ √₉ = 2 √₉ = 2 × 3 = 6. Therefore, this is not the correct expression.
Option 3: 2 √6
Here, we have the square root of 6. Since there are no other operations involved, this is not equivalent to 24 raised to the power of one-third.
Option 4: 2 √₃√₆
This option consists of the cube root of 6, multiplied by the cube root of 6. By multiplying the cube roots together, we get: ∛(6 × 6) = ∛36. Now, we need to simplify 24⁽¹⁄₃⁾.
To simplify 24⁽¹⁄₃⁾, we need to find the cube root of 24. The cube root of 24 can be written as: ∛24 = 2∛6.
Therefore, option 4 simplifies to 2 × 2∛6 = 4∛6.
So, the expression that is equivalent to 24 raised to the power of one-third is: 4√₆.