Question

Solve the equation p³ = -512. What are the possible values of p?

1) p = ±8
2) p = -8
3) p = ±23
4) p = -23

Answer 1

To solve the equation p³ = -512 and find the possible values of p, we need to find the cube root of -512. The cube root of -512 is -8, so p = -8 is the correct answer. 2) p = -8 is the correct answer.

Step-by-step explanation:

To solve the equation p³ = -512, we need to find the cube root of -512. The cube root of -512 can be written as p = -8 because -8 x -8 x -8 = -512. Therefore, the possible value of p is p = -8. So option 2) p = -8 is the correct answer.

Answer 2

The equation p³ = -512 has one real solution since cube roots have a single real value. By finding the cube root of -512, which is -8, it has been determined that the value of p is -8.(Option 2)

Step-by-step explanation:

To solve the equation p³ = -512, we need to find the cube root of -512. Since cube roots give us the number that, when multiplied by itself three times, results in the original number, and considering that multiplying three negative numbers together will give a negative result, we can deduce that the cube root of a negative number is also negative.

Now, if we think about the number 8, we know that 8³ = 512. Since we are looking for the negative cube root, the answer in this case would be -8, because (-8)³ = -8 × -8 × -8 = -512. There is only one real solution for the cube root of a real number, thus the only possible value of p is -8. Option 2 is the correct choice.