Question

Which expression is equivalent to x1/2y5/2 in simplified form?

A. radical xy^5
B. radical xy
C.y^2 radical xy
D.y^4 radical xy

Answer 1

The given expression when reduced in simplified form, reduces to

`=x^{(1)/(2)}* y^{(5)/(2)}\\\\=x^{(1)/(2)}* y^{(1)/(2)}* y^(2)\\\\=y^2√(xy)\\\\=y^2{\text{radical}}(x y)`

or

`=x^{(1)/(2)}* y^{(5)/(2)}\\\\={\text{Radical}}(x* y^5)`

Here, Radical = Square root

Used the following law of indices

`a^{(1)/(2)}=√(a)`

Option C: y²*Radical (x y)

Radical =Either Square root, or cube root ,.....fifth root,....

Option A :
`{\text{Radical}}(x* y^5)`

Answer 2

x^1/2 y^5/2 = (xy)^1/2 * y^2 = y^2 radical xy.