Question

Which expression is equivalent to ^4√16x^11y^8/81x^7y^6 ? Assume x > 0 and y = 0

Answer 1

 For this case we have an expression of the form:
 $\sqrt[4]{16x^{11}y^8}/(81x^7y^6)$
 To solve the problem, we must rewrite the expression using properties of exponents.
 Rewriting the expression we have:
 $\sqrt[4]{2^4x^8x^3y^8}/(81x^7y^6)$
 Then, by root properties we have:
 $2x^2y^2(\sqrt[4]{x^3})/(81x^7y^6)$
 Then, by power properties again:
 $2(\sqrt[4]{x^3})/(81x^5y^4)$
 Answer: 
 An expression that is equivalent is:
 $2(\sqrt[4]{x^3})/(81x^5y^4)$