Question

Which expression is equivalent to (4mn/m^-2n^6)^-2

Answer 1

First, we get rid of the negative exponent in the parenthesis.  We do this by moving it to the top.  Our equation is now:

$( \frac{4m^3n}{n^6})^{-2}$

Next, we can cross out one n from both the top and the bottom.

$(\frac{4m^3}{n^5} )^{-2}$

Finally, we evaluate the -2

Our equation becomes:

$\frac{ (4*m^3)^{-2} }{(n^5) ^{-2} }$

This becomes: $\frac{(n^5)^2}{(4*m^3)^2} = \frac{ n^{10} }{16*m^6}$

This can not be simplified any further, so this is the final answer.