Question

Which expression is equivalent to ? Assume x 0 and .

Answer 1

9514 1404 393

Answer:

`\frac{2x\sqrt[4]{y^2}}{3}`

Explanation:

We can first simplify under the radical, then take the 4th root.

`\sqrt[4]{(16x^(11)y^8)/(3x^7y^6)}=\sqrt[4]{(2^4x^((11-7))y^((8-6)))/(3^4)}=\sqrt[4]{((2x)^4)/(3^4)y^2}=\boxed{\frac{2x\sqrt[4]{y^2}}{3}}`

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The applicable rules of exponents are ...

(a^b)/(a^c) = a^(b-c)

(a^b)^c = a^(bc)

nth root is the same as an exponent of 1/n.