+112 Simplify \(^{x\sqrt{y}}/_{y\sqrt{x}}\) if \(x>0\) and \(y>0\).
A. \(^{\sqrt{y}}/_{xy}\)
B. \(^{\sqrt{y}}/_y\)
C. \(^{\sqrt{xy}}/_y\)
D. \(^{x\sqrt{xy}}/_y\)
P.S. this is different than Plato Classroom Question #13; it has variables instead of numbers and variables.
+129852 [ x √y ] / [ y √ x ]
Write in exponential form
[ x * y^1/2 ] / [ y * x^1/2 ] and we can write
[ x^1 / x^1/2 ] * [ y^1/2 / y^1 ]
Remember that a^m / a^n = a^( m - n)
So we have
x^(1 - 1/2) * y^(1/2 - 1)
x^1/2 * y^(-1/2) =
√x / √y multiply top/bottom by √y
[ √ x√ y ] / y
√[ xy] / y ⇒ "C"
