# How do you simplify #³sqrt(24w^2)# divided by #³sqrt(3w^4)#?

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To simplify ³√(24w^2) divided by ³√(3w^4), we can combine the two radicals by using the quotient rule of radicals. This rule states that the ³√(a) divided by ³√(b) is equal to the ³√(a/b).

Applying this rule to the given expression, we have:

³√(24w^2) / ³√(3w^4) = ³√(24w^2 / 3w^4)

Simplifying the expression inside the radical, we divide the coefficients and subtract the exponents of the variables:

³√(24w^2 / 3w^4) = ³√(8 / w^2)

Since 8 is a perfect cube (2^3), we can simplify further:

³√(8 / w^2) = 2 / ³√(w^2)

Therefore, the simplified form of ³√(24w^2) divided by ³√(3w^4) is 2 / ³√(w^2).

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