Simplify, giving solution with positive index
$(- a^{5}) (a^{2})$

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Solution

Step: simplifying using laws of exponents

Given, $(- a^{5}) (a^{2})$
It can be written as:
$(- 1 \times a^{5}) \times a^{2}$
On further calculation
$(- a^{5}) (a^{2}) = (- 1) \times a^{5 + 2}$ [ $∵ a^{m} \times a^{n} = a^{m + n}$ ]
$= - 1 \times a^{7}$
$= - a^{7}$

Hence, $(- a^{5}) (a^{2}) = - a^{7}$ .

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