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

Question

asked May 14, 2023 161k views

1 Answer

Epifanio · Answer 1 · 2023-05-19T21:20:48+0000

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

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