Question

Simplify this expression:
`((m^5n^5)^ (1)/(6) )/(3(mn)^ (-1)/(6) )`

Answer 1

1/3 x m^(2/3) x n^(2/3)

Answer 2

The simplify form of the expression is
`(mn)/(3)`.

Explanation:

Consider the provided expression.

`((m^5n^5)^(1)/(6) )/(3(mn)^ (-1)/(6))`

Apply the exponent rule:
`(ab)^c=a^cb^c`

Therefore,

`\frac{m^{(5)/(6)}n^{(5)/(6)}}{3m^{-(1)/(6)}n^{-(1)/(6)}}`

`\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=x^(a-b)`

`\frac{n^{(5)/(6)-(-(1)/(6))}m^{(5)/(6)-\left(-(1)/(6)\right)}}{3}`

`(mn)/(3)`

Therefore, the simplify form of the expression is
`(mn)/(3)`.