Question

Which expression is equivalent to (2x2)(3x3)(4x)2?

24x^7
48x^7
96x^7
576x^12

Answer 1

`96x^7`

Explanation:

To obtain the polynomial form we apply the distributive property .

Powers property

to multiply powers of different bases.

The bases are multiplied and the exponents are added

`(2x^2)(3x^3)(4x)^2= 6x^5(16x^2)\\ 6x^5(16x^2)=96x^7`

`(2x^2)(3x^3)(4x)^2=96x^7`

Answer 2

`96x^7`

Explanation:

Remember the following properties:

Multiplication of powers of equal base:

`x^n*x^m=x^(n+m)`

In this case we have the following expression:

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

`(2x^2)(3x^3)(16x^2)`

When applying the mentioned property we obtain the following

`(2*3*16x^(2+3+2))`

Simplifying we get:

`(96x^(7))`

The answer is the third option