Question

Which expression is equivalent to (3m^-2n)^-3/6mn^-2

Answer 1

      3^-3m^6n^-3
= ---------------------
          6mn^-2

          m^5
= --------------------
   3^3 * 6 n^3*n^-2

     m^5
= ------------
   162 n

answer is A. first one

Answer 2

Answer:

Option A. $\frac{m^{5} }{162n}$.

Step-by-step explanation:

The given expression is $\frac{(3m^{-2}.n)^{-3}}{6mn^{-2} }$

Now we have to simplify the expression.

$\frac{(3m^{-2}.n)^{-3}}{6mn^{-2}}=\frac{(3)^{-3}(m^{-2})^{-3}(n)^{-3}}{6mn^{-2}}$

=$\frac{(3)^{-3}.(m^{6}).n^{-3}}{6m.n^{-2}}=\frac{m^{6}.n^{-3}.m^{-1}.n^{2}}{6.3^{3}}$

=$\frac{m^{(6-1)}.n^{(2-3)}}{162}=\frac{m^{5}.n^{-1} }{162}=\frac{m^{5} }{162n}$

Therefore Option A. is the correct answer.