Question

Simplify this expression: $\frac{(m^5n^5)^ \frac{1}{6} }{3(mn)^ \frac{-1}{6} }$

Answer 1

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

Answer 2

Answer:

The simplify form of the expression is $\frac{mn}{3}$.

Step-by-step explanation:

Consider the provided expression.

$\frac{(m^5n^5)^\frac{1}{6} }{3(mn)^ \frac{-1}{6}}$

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

Therefore,

$\frac{m^{\frac{5}{6}}n^{\frac{5}{6}}}{3m^{-\frac{1}{6}}n^{-\frac{1}{6}}}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

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

$\frac{mn}{3}$

Therefore, the simplify form of the expression is $\frac{mn}{3}$.