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

Option A.
`(m^(5) )/(162n)`.

Explanation:

The given expression is
`((3m^(-2).n)^(-3))/(6mn^(-2) )`

Now we have to simplify the expression.

`((3m^(-2).n)^(-3))/(6mn^(-2))=((3)^(-3)(m^(-2))^(-3)(n)^(-3))/(6mn^(-2))`

=
`((3)^(-3).(m^(6)).n^(-3))/(6m.n^(-2))=(m^(6).n^(-3).m^(-1).n^(2))/(6.3^(3))`

=
`(m^((6-1)).n^((2-3)))/(162)=(m^(5).n^(-1) )/(162)=(m^(5) )/(162n)`

Therefore Option A. is the correct answer.