Use the distributive property to remove the parentheses. \[ 5 b^{9}\left(2 b^{6}+9 b\right) \]

To apply the distributive property, you multiply \(5 b^{9}\) by each term inside the parentheses. So, let's break it down: 1. Multiply \(5 b^{9}\) by \(2 b^{6}\): \[ 5 b^{9} \cdot 2 b^{6} = 10 b^{15} \] 2. Now, multiply \(5 b^{9}\) by \(9 b\): \[ 5 b^{9} \cdot 9 b = 45 b^{10} \] Putting it all together, the expression without parentheses is: \[ 10 b^{15} + 45 b^{10} \]