Simplify the equation (3mn)^(2) * (3m ^(3) n)^(4)

Question

Simplify the equation
`(3mn)^(2) * (3m ^(3) n)^(4)`

Answer 1

The expression becomes;

`216s^(15)t^(18)`

Step-by-step explanation:

Simplify the expression;

`(6s^5t^6)^3`

Applying the laws of indices;

Power of power rule;

`(a^m)^n=a^(mn)`

The expression becomes;

`\begin{gathered} (6s^5t^6)^3 \\ =(6)^3(s^5)^3(t^6)^3 \\ =6^3s^(5(3))t^(6(3)) \\ =6^3s^(15)t^(18) \end{gathered}`

Therefore, the expression becomes;

`216s^(15)t^(18)`