Question

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

Answer 1

Given: The equation $(4x^{3})(2x)^{-4}$

To Find: The simplified expression

Solution: $\frac{1}{4x}$

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

$4x^{3}(2x)^{-4} \\\\= \frac{4x^{3}}{(2x)^{4}} \\\\=\frac{4x^{3}}{16x^{4}}\\\\=\frac{1}{4}x^{3-4} \\\\=\frac{1}{4}x^{-1}\\\\ =\frac{1}{4x}$

We have used two Rules of Exponents

1. For any integer a, $x^{-a}= \frac{1}{x^{a}}$
2. And for any integers a, b, $x^{a-b}= \frac{x^a}{x^b}$

Answer 2

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