High School

What is the product?

[tex](4x)(-3x^8)(-7x^3)[/tex]

A. [tex]-84x^{12}[/tex]
B. [tex]-84x^{24}[/tex]
C. [tex]84x^{12}[/tex]
D. [tex]84x^{24}[/tex]

Answer :

To simplify the expression
[tex]$$
(4x)(-3x^8)(-7x^3),
$$[/tex]
we can follow these steps:

1. Multiply the numerical coefficients:
[tex]$$4 \times (-3) = -12,$$[/tex]
then:
[tex]$$-12 \times (-7) = 84.$$[/tex]

2. Combine the powers of [tex]$x$[/tex]. When multiplying like bases, we add the exponents:
[tex]$$x^{1} \cdot x^{8} \cdot x^{3} = x^{1+8+3} = x^{12}.$$[/tex]

3. Therefore, the final product is:
[tex]$$84x^{12}.$$[/tex]

Thus, the answer is:

[tex]$$84x^{12}.$$[/tex]