Question

What is the simplified form of (2x^1/2y^2/3)(4x^1/4y^5/6).

Answer 1

The simplified form is:
`(1)/(2)x^{(1)/(4)}y^{-(1)/(6)}` or
`\frac{x^{(1)/(4)}}{2y^{(1)/(6)}}`

Explanation:

So we need to find the simplified form of:

`\frac{2x^{(1)/(2)}y^{(2)/(3)}}{4x^{(1)/(4)}y^{(5)/(6)}}`

We know that:

(a^m)/(a^n) = a^(m-n)

Then:

`(2)/(4)x^{(1)/(2) - (1)/(4) }y^{(2)/(3)-(5)/(6)}`

Simplifien the expression:

`(1)/(2)x^{(1)/(4)}y^{-(1)/(6)}`

So, the simplified form is:

`(1)/(2)x^{(1)/(4)}y^{-(1)/(6)}` or
`\frac{x^{(1)/(4)}}{2y^{(1)/(6)}}`