${(\frac{b^{- 3} \cdot b^{7} \cdot (b^{- 1})^{2}}{(- b)^{2} \cdot (b^{2})^{3}})}^{- 2}$ .

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Solution

${(\frac{b^{- 3} b^{7} ({b^{- 1})}^{2}}{{(- b)}^{2} (b^{2})^{3}})}^{- 2} = {(\frac{b^{- 3} b^{7} b^{- 2}}{b^{2} b^{6}})}^{- 2} = {(\frac{(b^{- 3 + 7 - 2})}{b^{(2 + 6)}})}^{- 2} = {(\frac{b^{2}}{b^{8}})}^{- 2} = {(b^{(2 - 8)})}^{- 2} = {(b^{- 6})}^{- 2} = b^{12}$

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