\( \left. \begin{array} { | l l | } \hline \text { Activity 3: Fully simplify the following expressions. } \\ { 3.1 } & { ( y ^ { 3 } ) ^ { 4 } } \\ { 3.2 } & { 2 ( m ^ { 4 } ) ^ { \frac { 1 } { 3 } } } \\ { 3.3 } & { 4 ( 4 x ^ { 2 } ) ^ { 3 } } \end{array} \right. \)

Let's simplify each expression step by step: For \( ( y ^ { 3 } ) ^ { 4 } \): Using the power of a power rule, \( (a^m)^n = a^{m \cdot n} \), we get: \[ ( y ^ { 3 } ) ^ { 4 } = y^{3 \cdot 4} = y^{12} \] For \( 2 ( m ^ { 4 } ) ^ { \frac { 1 } { 3 } } \): Again applying the power of a power rule, we have: \[ 2 ( m ^ { 4 } ) ^ { \frac { 1 } { 3 } } = 2 m^{4 \cdot \frac{1}{3}} = 2 m^{\frac{4}{3}} \] For \( 4 ( 4 x ^ { 2 } ) ^ { 3 } \): First, simplify the expression inside the parentheses: \[ ( 4 x ^ { 2 } ) ^ { 3 } = 4^3 ( x ^ { 2 } )^3 = 64 x^{6} \] Now multiply by 4: \[ 4 \cdot 64 x^{6} = 256 x^{6} \] So the simplified results are: 3.1: \( y^{12} \) 3.2: \( 2 m^{\frac{4}{3}} \) 3.3: \( 256 x^{6} \)