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)`