Daniel O. | Math and Physics Tutor, with a math and physics degreeMath and Physics Tutor, with a math and ...

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Diana, you could rewrite your problem like so (when you have a negative exponent in the numerator, take the reciprocal of it to make it positive in the denominator):

3(x+1)^{-2/3} = 3/(x+1)^{2/3}

so now we have 3/(x+1)^{2/3} = 0

Now we have it as a fraction, with numerator 3 and denominator (x+1)^{2/3}. From here we can see that no value of x will give us an answer of 0 - since there is no denominator that will yield an answer of zero when divided into 3.

The only way a fraction can be equal to zero is if the numerator is equal to zero (but not also the denominator, as 0/0 is undefined).

x = -1 isn't a valid solution, since when you substitute it back into the original equation, you'll have 0^(-2/3) which is undefined. Though, when you took both sides to the power of -3/2, that should give the right hand side as 0^(-3/2), which is undefined and prevents you from reaching a value for x.

## Comments

x = -1 isn't a valid solution, since when you substitute it back into the original equation, you'll have 0^(-2/3) which is undefined. Though, when you took both sides to the power of -3/2, that should give the right hand side as 0^(-3/2), which is undefined and prevents you from reaching a value for x.

Ah, you're right. I neglected the negative sign when I gave that solution