Simplify and express the answer in the positive exponent form:(vi) $(a^{3} b^{- 5})^{- 2}$

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Solution

Given : $(a^{3} b^{- 5})^{- 2}$
It can be written as:
$(a^{3} b^{- 5})^{- 2} = a^{3 \times - 2} b^{- 5 \times - 2}$
[ $∵$ $(a b)^{m} = a^{m} b^{m}$ ]
$= a^{- 6} b^{10}$
$= \frac{b^{10}}{a^{6}}$
Hence, $(a^{3} b^{- 5})^{- 2} = \frac{b^{10}}{a^{6}}$ .

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