The simplified expression of [tex]$4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3}[/tex] is [tex]4x^3[/tex].
Solution:
Given expression is [tex]4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3}[/tex].
To simplify the given expression.
[tex]$\Rightarrow4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3}[/tex]
Using exponent rule: [tex]\frac{1}{a^{-m}}=a^m[/tex]
[tex]$\Rightarrow4x \cdot x^{5}.x^{-3}[/tex]
Using another exponent rule: [tex]a^m \cdot a^n=a^{m+n}[/tex]
[tex]$\Rightarrow4x \cdot x^{5-3}[/tex]
[tex]$\Rightarrow4x \cdot x^{2}[/tex]
Using exponent rule: [tex]a^m \cdot a^n=a^{m+n}[/tex]
[tex]$\Rightarrow4x^{1+2}[/tex]
[tex]$\Rightarrow4x^3[/tex]
Hence the simplified expression of [tex]$4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3}[/tex] is [tex]4x^3[/tex].
