Simplifying Exponents

Question

(x^1/2 y / y^1/2)^{3 =}

^{y^3 x ^3/2 / y^3/2}

^{I am told the answer is x^3/2 / y 3/2}

^{Where did the y^3 in the numerator go?}

Answer 1

The person who gave you that answer "lost" the y³ in the numerator!

(x^1/2 y / y^1/2)³ = (x^1/2 y)³ / ( y^1/2)³ = x^3/2y³ / y^3/2 = x^3/2 y^3-3/2 = x^3/2y^6/2-3/2 = x^3/2y^3/2 = (xy)^3/2