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

The correct answer is
`(1)/(4x)`

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)=(1)/((2x)^(4))=(1)/(16x^(4))` (II)

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

`(4x^(3)).((1)/(16x^(4)))`

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

`(4x^(3)).((1)/(16x^(4)))=(4x^(3))/(16x^(4))=(1)/(4x)`

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