Use the exponent properties to simplify the following ((3x^2)^3)/((2x)^4)

Question

Use the exponent properties to simplify the following

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

Answer 1

`(27)/(16)x^2`

Explanation:

The relevant properties are ...

(a^b)^c = a^(bc)

(a^b)/(a^c) = a^(b-c)

So, the expression simplifies to ...

`((3x^2)^3)/((2x)^4)=(3^3x^(2\cdot 3))/(2^4x^4)=(27)/(16)x^(6-4)=(27)/(16)x^(2)`