Answer:
[tex]5\ x^6[/tex]
Step-by-step explanation:
Given expression:
[tex]5x\ .\ \frac{1}{x^{-7}}\ .\ x^{-2}[/tex]
Rules of exponents to be used:
[tex]a^{-b}=\frac{1}{a^b}[/tex] [Rule of negative exponent]
[tex]a^b\ .\ a^c=a^{b+c}[/tex] [Product Rule]
Using the above rules to simplify the given expression.
⇒ [tex]5x\ .\frac{1}{\frac{1}{x^7}}\ .\ x^{-2}[/tex] [By rule of negative exponent]
⇒ [tex]5x\ .\ x^7\ .\ x^{-2}[/tex] [Simplifying fractions]
⇒ [tex]5\ x^{1+7-2}[/tex] [By product rule]
⇒ [tex]5\ x^6[/tex] (Answer)
