Simplify. \[ 2 v^{-6} \cdot 9 w u^{-6} \cdot 5 u^{6} v^{9} w^{-8} \] Use only positive exponents in your answer.

Calculate or simplify the expression \( 2v^{-6} * 9w * u^{-6} * 5u^{6} * v^{9} * w^{-8} \). Simplify the expression by following steps: - step0: Solution: \(2v^{-6}\times 9wu^{-6}\times 5u^{6}v^{9}w^{-8}\) - step1: Multiply the terms: \(90v^{-6}wu^{-6}\times u^{6}v^{9}w^{-8}\) - step2: Multiply the terms: \(90v^{-6+9}wu^{-6}\times u^{6}w^{-8}\) - step3: Add the numbers: \(90v^{3}wu^{-6}\times u^{6}w^{-8}\) - step4: Multiply the terms: \(90v^{3}w^{1-8}u^{-6}\times u^{6}\) - step5: Subtract the numbers: \(90v^{3}w^{-7}u^{-6}\times u^{6}\) - step6: Multiply the terms: \(90v^{3}w^{-7}u^{-6+6}\) - step7: Add the numbers: \(90v^{3}w^{-7}u^{0}\) - step8: Evaluate the power: \(90v^{3}w^{-7}\) - step9: Simplify: \(\frac{90v^{3}}{w^{7}}\) The simplified expression is \(\frac{90v^{3}}{w^{7}}\).