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

Question

asked Nov 25, 2021 118k views

1 Answer

Seth Carnegie · Answer 1 · 2021-12-01T11:55:45+0000

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)