((1)/(4) m^(2) n)^(3) * (-32m^(2)n) PLEASE PROVIDE AN EXPLANATION, I'M UNSURE OF HOW TO FIND THE ANSWER

Question

`((1)/(4) m^(2) n)^(3) * (-32m^(2)n)`

PLEASE PROVIDE AN EXPLANATION, I'M UNSURE OF HOW TO FIND THE ANSWER

Answer 1

`\bold{(\frac14m^2n)^3*(-32m^2n)=-\frac12m^8n^4}`

Explanation:

`(\frac14m^2n)^3*(-32m^2n)=\\\\=(\frac14)^3*(m^2)^3*n^3*(-32)*m^2*n=\\\\= \frac1{64}*m^(2\cdot3)*n^3*(-32)*m^2*n=\\\\= \frac1{64}*(-32)*m^(6)*m^2*n^3*n=\\\\=-(32)/(64)*m^(6+2)*n^(3+1)=\\\\=-\frac12m^8n^4`