Answer:
The correct answer is [tex]\frac{1}{4x}[/tex]
Step-by-step explanation:
Let's start writing the expression :
[tex](4x^{3}).(2x)^{-4}[/tex] (I)
In order to find an equivalent expression, we first need to solve the exponential term on the right.
Let's write it and solve it :
[tex](2x)^{-4}=\frac{1}{(2x)^{4}}=\frac{1}{16x^{4}}[/tex] (II)
Now, we need to replace (II) in (I) :
[tex](4x^{3}).(\frac{1}{16x^{4}})[/tex]
The final step is to distribute the multiplication and make some simplifications :
[tex](4x^{3}).(\frac{1}{16x^{4}})=\frac{4x^{3}}{16x^{4}}=\frac{1}{4x}[/tex]
Let's remember that we can simplify the numbers between numbers and the ''x'' between ''x''.
