b) \( \left(2 n^{2} y^{10}\right)^{3}\left(3 n^{8} y^{6}\right)^{2} \)

Let’s break down the expression \( \left(2 n^{2} y^{10}\right)^{3}\left(3 n^{8} y^{6}\right)^{2} \) step by step. First, we will handle each part separately: 1. For \( \left(2 n^{2} y^{10}\right)^{3} \): - \( 2^{3} = 8 \) - \( n^{2 \cdot 3} = n^{6} \) - \( y^{10 \cdot 3} = y^{30} \) Therefore, \( \left(2 n^{2} y^{10}\right)^{3} = 8 n^{6} y^{30} \). 2. For \( \left(3 n^{8} y^{6}\right)^{2} \): - \( 3^{2} = 9 \) - \( n^{8 \cdot 2} = n^{16} \) - \( y^{6 \cdot 2} = y^{12} \) Thus, \( \left(3 n^{8} y^{6}\right)^{2} = 9 n^{16} y^{12} \). Now we can combine both parts: \[ 8 n^{6} y^{30} \cdot 9 n^{16} y^{12} \] Multiplying the constants together: \[ 8 \cdot 9 = 72 \] Next, we combine the \( n \) terms: \[ n^{6} \cdot n^{16} = n^{6 + 16} = n^{22} \] And for the \( y \) terms: \[ y^{30} \cdot y^{12} = y^{30 + 12} = y^{42} \] Putting it all together, we get: \[ 72 n^{22} y^{42} \] So, the fully simplified expression is: \[ 72 n^{22} y^{42} \]