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

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

Answer 2

Answer:

The given expression when reduced in simplified form, reduces to

$=x^{\frac{1}{2}}\times y^{\frac{5}{2}}\\\\=x^{\frac{1}{2}}\times y^{\frac{1}{2}}\times y^{2}\\\\=y^2\sqrt{xy}\\\\=y^2{\text{radical}}(x y)$

or

$=x^{\frac{1}{2}}\times y^{\frac{5}{2}}\\\\={\text{Radical}}(x\times y^5)$

Here, Radical = Square root

Used the following law of indices

$a^{\frac{1}{2}}=\sqrt{a}$

Option C: y²*Radical (x y)

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

Option A : ${\text{Radical}}(x\times y^5)$