Experiments with iframe and MathML by Grindle

Simplify. Express your answer with positive exponents only.

Method 1:

{(\frac{6 b^{- 3} c^{- 2}}{2 b^{- 5} c^{- 2}})}^{- 2} = {(\frac{6}{2} \cdot \frac{b^{- 3}}{b^{- 5}} \cdot \frac{c^{- 2}}{c^{- 2}})}^{- 2} = {(\frac{3}{1} \cdot \frac{b^{2}}{1} \cdot \frac{1}{1})}^{- 2} = {(\frac{3 b^{2}}{1})}^{- 2} = \frac{1}{{(3 b^{2})}^{2}} = \frac{1}{9 b^{4}}

Method 2:

{(\frac{6 b^{- 3} c^{- 2}}{2 b^{- 5} c^{- 2}})}^{- 2} = {(\frac{6}{2} \cdot \frac{b^{- 3}}{b^{- 5}} \cdot \frac{c^{- 2}}{c^{- 2}})}^{- 2} = {(\frac{6}{2} \cdot b^{(^{-} 3 -^{−} 5)} \cdot c^{(^{-} 2 -^{-} 2)})}^{^{-} 2} = {(3 \cdot b^{(^{-} 3 + 5)} \cdot c^{(^{-} 2 + 2)})}^{^{-} 2} = {(3 \cdot b^{2} \cdot c^{0})}^{^{-} 2} = \frac{1}{{(3 b^{2})}^{2}} = \frac{1}{9 b^{4}}

the end