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^{\frac{n}{m}}$$(x^m)^n=x^{m\cdot n}$$x^m\cdot x^n=x^{m+n}$

so we can simplify the expression as

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

the expression simplified is

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