The expression that is equivalent to [tex]\left(4 x^{3}\right)(2 x)^{-4}[/tex] is [tex]\frac{1}{4 x}[/tex]
Step-by-step explanation:
Given Expression:
[tex]\left(4 x^{3}\right)(2 x)^{-4}[/tex]
To find: The simplified expression
Use the Rules of Exponents, to simply the given equation as below,
[tex]\left(4 x^{3}\right)(2 x)^{-4}[/tex]
Rule 1: Rules of Exponents [tex]x^{-a}=\frac{1}{x^{a}}[/tex]
[tex](2 x)^{-4}[/tex] can be written as [tex]\frac{1}{(2 x)^{4}}[/tex] . So, the equation would be
[tex]\frac{4 x^{3}}{(2 x)^{4}}[/tex]
Rule 2: Rules of Exponents [tex]x^{a-b}=\frac{x^{a}}{x^{b}}[/tex]. then
[tex]\frac{4 x^{3}}{(2 x)^{4}}=\frac{4 x^{3}}{16 x^{4}}=\frac{1}{4} x^{3-4}=\frac{1}{4} x^{-1}=\frac{1}{4 x}[/tex]
