Question

Solve (v⁵)³ - 16 = 0, where v is a real number. Write your answer in simplified radical form.

Answer 1

The solution to the equation (v⁵)³ - 16 = 0 in simplified radical form is v = ±4. This is obtained by isolating the cube on one side, taking the cube root, and then taking the fifth root of the result.

Step-by-step explanation:

To solve the equation (v⁵)³ - 16 = 0 where v is a real number, we can follow these steps:

1. Add 16 to both sides to isolate the cube on one side: (v⁵)³ = 16.
2. Take the cube root of both sides to solve for v⁵: v⁵ = ³√16.
3. Since 16 is a perfect square (4²), we find that v⁵ is equal to 4, because 4² = 16 and we are searching for the cube root.
4. To find the value of v, take the fifth root of 4. Noting that a root can be positive or negative, we find that v = ±4.

Therefore, the solution to the equation in simplified radical form is v = ±4.