Simplifying Radicals?

Question

Sqrt(x^3y^9) = xy^4sqrt(xy)

Sqrt(x^9y^9) = x^4y^4sqrt(xy)

The ^ is where the number should be an exponet to the number it.
Now explain how the answer is what it is plz.

Answer 1

sqrt(x) is the same as x^(1/2)
so Sqrt(x^3y^9) is the same as
(x^3y^9)^(1/2)
and this is equal to (x^3)^(1/2) * (y^9)^(1/2).
Now,
(x^3)^(1/2)=
x^(3/2)=
x*x^(1/2)=
x sqrt(x)
and
(y^9)^(1/2)=
y^(9/2)=
y*y*y*y*y^(1/2)=
y^4 sqrt(y)
so (x^3)^(1/2)(y^9)^(1/2)=
xy^4sqrt(xy)

Answer 2

Factor out.

Sqrt(x^3y^9) factor out xy, to start, though you could bite deeper

xysqrt(x^2y^8) looking more tractable?

bring out y^8, x^2 and you see

xy^4sqrt(xy)

Answer 3

sqrt(x^3y^9) =
sqrt(x^2 * y^8 * xy) =
(x^2y^8)^(1/2) * sqrt(xy) =
x^(2 * (1/2)) * y^(8 * (1/2)) * sqrt(xy) =
xy^4sqrt(xy)

-----------------------

sqrt(x^9y^9) =
sqrt(x^8 * y^8 * xy) =
(x^8y^8)^(1/2) * sqrt(xy) =
x^4y^4sqrt(xy)