Answer:
[tex](D)x^{3/4}y^{1/2}[/tex]
Step-by-step explanation:
We are required to simplify the expression: [tex](x^{1/2}y^{1/3})(x^{1/4}y^{1/6})[/tex]
This is a product and the first thing we will do is to collect like terms:
[tex](x^{1/2}y^{1/3})(x^{1/4}y^{1/6})=x^{1/2}x^{1/4}y^{1/3}y^{1/6}[/tex]
Next, we apply the addition law of indices: [tex]x^a X x^b =x^{a+b}[/tex]
[tex]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}[/tex]
Therefore, [tex](x^{1/2}y^{1/3})(x^{1/4}y^{1/6})=x^{3/4}y^{1/2}[/tex]
