Simplify. \( 9 x^{5}+8\left(4 x^{5}-6 b^{3}\right) \)

To simplify the expression \( 9 x^{5}+8\left(4 x^{5}-6 b^{3}\right) \), let's start by distributing the 8 across the terms inside the parentheses: \[ 9 x^{5} + 8 \cdot 4 x^{5} - 8 \cdot 6 b^{3} \] This gives us: \[ 9 x^{5} + 32 x^{5} - 48 b^{3} \] Now, combine the like terms \(9 x^{5}\) and \(32 x^{5}\): \[ (9 + 32)x^{5} - 48 b^{3} = 41 x^{5} - 48 b^{3} \] So, the simplified form of the expression is: \[ 41 x^{5} - 48 b^{3} \]