Middle School

Which expression is equivalent to [tex](2x^2)(3x^3)(4x)^2[/tex]?

A. [tex]24x^7[/tex]
B. [tex]48x^7[/tex]
C. [tex]96x^7[/tex]
D. [tex]576x^{12}[/tex]

Answer :

Answer:

[tex]96x^7[/tex]

Step-by-step 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

[tex](2x^2)(3x^3)(4x)^2= 6x^5(16x^2)\\ 6x^5(16x^2)=96x^7[/tex]

[tex](2x^2)(3x^3)(4x)^2=96x^7[/tex]

Answer:

[tex]96x^7[/tex]

Step-by-step explanation:

Remember the following properties:

Multiplication of powers of equal base:

[tex]x^n*x^m=x^{n+m}[/tex]

In this case we have the following expression:

[tex](2x^2)(3x^3)(4x)^2[/tex]

[tex](2x^2)(3x^3)(16x^2)[/tex]

When applying the mentioned property we obtain the following

[tex](2*3*16x^{2+3+2})[/tex]

Simplifying we get:

[tex](96x^{7})[/tex]

The answer is the third option