State True or False.
Simplifying and expressing as positive indices $(a^{- 2} b)^{- 2} \times (a b)^{- 3}$ , we get $\frac{a}{b^{5}}$ .

True

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False

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Solution

The correct option is A True
As given $(a^{- 2} b)^{- 2} . (a b)^{- 3}$

$\Rightarrow (a^{- 2 \cdot - 2} b^{- 2}) . (a^{- 3} b^{- 3})$
$\Rightarrow (a^{4} b^{- 2}) . (a^{- 3} b^{- 3})$
$\Rightarrow a^{4 + (- 3)} b^{(- 2) + (- 3)}$
$\Rightarrow a^{4 - 3} . b^{- 2 - 3}$
$\Rightarrow a b^{- 5}$
$\Rightarrow \frac{a}{b^{5}}$

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