How do you simplify #(x^(1/3)+x^(-1/3))^2#?
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To simplify (x^(1/3) + x^(-1/3))^2, you need to expand the expression using the distributive property and then combine like terms.
First, square each term inside the parentheses:
(x^(1/3))^2 + 2(x^(1/3))(x^(-1/3)) + (x^(-1/3))^2
Simplify each term:
= x^(2/3) + 2(x^(1/3) * x^(-1/3)) + x^(-2/3)
= x^(2/3) + 2(x^(1/3 - 1/3)) + x^(-2/3)
= x^(2/3) + 2(x^(0)) + x^(-2/3)
= x^(2/3) + 2(1) + x^(-2/3)
= x^(2/3) + 2 + x^(-2/3)
Therefore, the simplified form of (x^(1/3) + x^(-1/3))^2 is x^(2/3) + 2 + x^(-2/3).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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