Question

Which expression is equivalent to (4x^3)(2x)^-4 1/4x 4/x 8/x 128/x

Answer 1

Hello : 
(4x^3)(2x)^-4=(4x^3) (2^-4)(x^-4)
=(4/16)(x^-1) = 1/4x

Answer 2

Answer:

The correct answer is  $\frac{1}{4x}$

Step-by-step explanation:

Let's start writing the expression :

$(4x^{3}).(2x)^{-4}$ (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 :

$(2x)^{-4}=\frac{1}{(2x)^{4}}=\frac{1}{16x^{4}}$ (II)

Now, we need to replace (II) in (I) :

$(4x^{3}).(\frac{1}{16x^{4}})$

The final step is to distribute the multiplication and make some simplifications :

$(4x^{3}).(\frac{1}{16x^{4}})=\frac{4x^{3}}{16x^{4}}=\frac{1}{4x}$

Let's remember that we can simplify the numbers between numbers and the ''x'' between ''x''.