Step-by-step explanation:
Given [tex]\frac{x*x^{-2} }{x^{13}}[/tex]
= [tex]\frac{x*x^{-2} }{x^{13}} = \frac{x^{-1} }{x^{13}}[/tex]
According to the Negative Exponent Rule, [tex]a^{-n} = \frac{1}{a^{n}}[/tex]
Therefore, [tex]\frac{x^{-1} }{x^{13}} = \frac{1}{x^{1}*x^{13}} = \frac{1}{x^{13+1}}= \frac{1}{x^{14}}[/tex]
In other words, [tex]x^{-1}[/tex] became positive because of the Negative Exponent Rule. Once you bring [tex]x^{-1}[/tex] down towards the denominator, you're essentially removing its negativity and turning its exponent into a positive value. Once that takes place, then you could apply the Product Rule of Exponents onto the exponents in the denominator, where it states, [tex]a^{m}a^{n} = a^{m+n}[/tex].
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