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

`(D)x^(3/4)y^(1/2)`

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)`

`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)`

Therefore,
`(x^(1/2)y^(1/3))(x^(1/4)y^(1/6))=x^(3/4)y^(1/2)`