Question

Which expression is equivalent to (4x3)(2x)-4

Answer 1

The expression that is equivalent to
`\left(4 x^(3)\right)(2 x)^(-4)` is
`(1)/(4 x)`

Explanation:

Given Expression:

`\left(4 x^(3)\right)(2 x)^(-4)`

To find: The simplified expression

Use the Rules of Exponents, to simply the given equation as below,

`\left(4 x^(3)\right)(2 x)^(-4)`

Rule 1: Rules of Exponents
`x^(-a)=(1)/(x^(a))`

`(2 x)^(-4)` can be written as
`(1)/((2 x)^(4))` . So, the equation would be

`(4 x^(3))/((2 x)^(4))`

Rule 2: Rules of Exponents
`x^(a-b)=(x^(a))/(x^(b))`. then

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