Question

Please answer the question in the photo.

Answer 1

Answer: Choice B

The equation is sometimes true. When x = 0, 1 or -1, then the equation is true. Otherwise, the equation is false.

====================================================

Step-by-step explanation:

When it comes to something like "always true" all we need is one counter example to break that statement. Pick something like x = 64 and you'll find that the left hand side becomes

`x^(1/3) = 64^(1/3) = \sqrt[3]{64} = \sqrt[3]{4^3} = 4`

while the right hand side turns into

`x^3 = 4^3 = 4*4*4 = 64`

This means the original equation
`x^(1/3) = x^3` updates to
`4 = 64` after plugging in x = 4. We get a false statement making the original statement false when x = 4. So saying "
`x^(1/3) = x^3` is always true" is not correct.

----------------------

The equation is only sometimes true for the x values 0, 1 and -1

Let's try x = 0

`x^(1/3) = x^3\\\\0^(1/3) = 0^3\\\\0 = 0`

we get a true statement confirming x = 0 as a solution

Trying x = 1 leads to

`x^(1/3) = x^3\\\\(1)^(1/3) = 1^3\\\\1 = 1`

also true. A similar situation happens with x = -1 as well, just that we have negatives this time.