Question

#54 Simplify and write the answers using positive exponents only.

Answer 1

gg easy

remember
(x^m)/(x^n)=x^(m-n)
and
(x^m)^n=x^(mn)
and
(xyz)^m=(x^m)(y^m)(z^m)
and
(m/n)^a=(m^a)/(n^a)
and
x^-n=1/(x^n)

so

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

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

`(2^(-3))((m^2)^(-3))((n^(-4))^(-3))`=

`( (1)/(2^3))(m^(-6))(n^(12))`=

`( (1)/(8) )( (1)/(m^6))(n^(12))`=

`(n^(12))/(8m^6)`