# How do you simplify #root3(y^6)/(root3(27y)*root3(y^11))#?

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To simplify the expression (root3(y^6))/(root3(27y)*root3(y^11)), we can start by simplifying the individual terms inside the roots.

First, let's simplify root3(y^6). Since the index of the root is 3, we can rewrite y^6 as (y^2)^3. Therefore, root3(y^6) simplifies to y^2.

Next, let's simplify root3(27y). We can rewrite 27 as 3^3, and since the index of the root is 3, we can rewrite root3(27y) as root3(3^3 * y) which simplifies to 3y.

Finally, let's simplify root3(y^11). Since the index of the root is 3, we can rewrite y^11 as (y^3)^3 * y^2. Therefore, root3(y^11) simplifies to y^3 * y^2, which is y^5.

Now, we can substitute these simplified terms back into the original expression:

(y^2) / (3y * y^5)

To simplify further, we can divide y^2 by y^5, which gives us 1/y^3. Therefore, the simplified expression is:

1 / (3y^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.

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