Simplifying Radicals (help!)

Question

(3sqrt(x^2)y^3)/(x^2)sqrt(y)

Rewrite in terms of fractional exponents and simplify

Answer 1

Since sqrt(x^2)=x, the equation becomes
3x(y^3)/(x^2)sqrt(y)
In exponential notation:
sqrt(y) is y^(1/2)
1/x^2 is x^(-2)
1/y^(1/2) is y^(-1/2)
So the equation becomes:
3x(y^3)(x^(-2))(y^(-1/2))
For any exponent, (z^a)(x^b)=z^(a+b), so the equation becomes
3x^(1-2)y^(3-1/2) = 3x^(-1)y^(2 1/2), or equivalently,
3y^2(sqrt(y)/x

Answer 2

sqrt(x²)/X² = 1/x = x^-1

 

y³/√y = y^5/2

 

Collecting 3x^-1y^5/2