Question

Simplify the expression. (x1/2y1/3)(x1/4y1/6) A) x1/2y1/2 B) x1/8y1/18 C) x2y2 D) x3/4y1/2

Answer 1

Answer:

$(D)x^{3/4}y^{1/2}$

Step-by-step explanation:

We are required to simplify the expression: $(x^{1/2}y^{1/3})(x^{1/4}y^{1/6})$

This is a product and the first thing we will do is to collect like terms:

$(x^{1/2}y^{1/3})(x^{1/4}y^{1/6})=x^{1/2}x^{1/4}y^{1/3}y^{1/6}$

Next, we apply the addition law of indices: $x^a X x^b =x^{a+b}$<u />

<u />$x^{1/2}x^{1/4}y^{1/3}y^{1/6}=x^{1/2+1/4}y^{1/3+1/6}\\\\=x^{3/4}y^{1/2}$<u />

Therefore, $(x^{1/2}y^{1/3})(x^{1/4}y^{1/6})=x^{3/4}y^{1/2}$