# How do you simplify (-4b^-3)(1/6b^2)(9b)^-4 and write it using only positive exponents?

Oct 14, 2017

$- \frac{2}{6561 {b}^{5}}$
$\left(- 4 {b}^{-} 3\right) \left(\left(\frac{1}{6}\right) {b}^{2}\right) {\left(9 b\right)}^{-} 4$
$= \left(- 4\right) \left(\frac{1}{6}\right) \left({9}^{-} 4\right) \left({b}^{-} 3 \cdot {b}^{2} \cdot {b}^{-} 4\right)$
$= - \left(\frac{2}{3}\right) \left(\frac{1}{9} ^ 4\right) \left({b}^{- 3 + 2 - 4}\right) = \left(- \frac{2}{6561}\right) \left({b}^{-} 5\right)$
$= - \frac{2}{6561 {b}^{5}}$