Question

Which expression is equivalent to (4x^3)(2x)^-4

Answer 1

(4x^3)(2x)^-4=(4x^3) (2^-4)(x^-4)
=(4/16)(x^-1) = 1/4x
The answer is 1/4x

Answer 2

Given: The equation
`(4x^(3))(2x)^(-4)`

To Find: The simplified expression

Solution:
`(1)/(4x)`

Calculation/Explanation: The equation can be simplified in the follwing way by using the Rules of Exponents.

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

We have used two Rules of Exponents

1. For any integer a,
   `x^(-a)= (1)/(x^(a))`
2. And for any integers a, b,
   `x^(a-b)= (x^a)/(x^b)`