Question

Simplify the expression below if x > 0 and y > 0.
x squareroot y Over y squareroot x

Answer 1

sorry I accidently closed. but please still answer

Answer 2

Recall that \(\sqrt{a}=a^{1/2}\). Now you can use the exponent laws which should simplify the problem

Answer 3

So: \[ \frac{x\sqrt{y}}{y\sqrt{x}}=\frac{xy^{1/2}}{yx^{1/2}}\]

Answer 4

Using the law: \[\large \frac{a^m}{a^n}=a^{m-n} \] we obtain:
\[ \frac{xy^{1/2}}{x^{1/2}y}=x^{1-\frac{1}{2}}y^{\frac{1}{2}-1}=x^{\frac{1}{2}}y^{-\frac{1}{2}}=\frac{x^{1/2}}{y^{1/2}}=\frac{\sqrt{x}}{\sqrt{y}}=\frac{\sqrt{x}}{\sqrt{y}}\frac{\sqrt{y}}{\sqrt{y}}=\frac{\sqrt{xy}}{y}\]

Answer 5

Thanks mate @kirbykirby

Answer 6

yw :)