Question

How can I simplify the expression with rational exponents and radicals (x^2y)^3 2^√y^4.

Answer 1

We have

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

we will use the next formulas in we can simplify the expression

`\sqrt[m]{x^n}=x^{(n)/(m)}`
`(x^m)^n=x^(m\cdot n)`
`x^m\cdot x^n=x^(m+n)`

so we can simplify the expression as

`(x^2y)^3\sqrt[]{y^4}=x^(3\cdot2)y^(3\cdot1)(y^{(4)/(2)})=x^6y^3y^2=x^6y^(3+5)=x^6y^5`

the expression simplified is

`(x^2y)^3\sqrt[]{y^4}=x^6y^5`