High School

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------------------------------------------------ What is the product?

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

A. [tex]-84x^{12}[/tex]

B. [tex]-84x^{24}[/tex]

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

D. [tex]84x^{24}[/tex]

Answer :

To solve the problem, we can follow these steps:

1. Multiply the numerical coefficients:

[tex]$$4 \times (-3) \times (-7) = 84$$[/tex]

2. Add the exponents of [tex]$x$[/tex] from each term. Since the first term is [tex]$4x$[/tex], it has an exponent of [tex]$1$[/tex]. The second term [tex]$-3x^8$[/tex] has an exponent of [tex]$8$[/tex], and the third term [tex]$-7x^3$[/tex] has an exponent of [tex]$3$[/tex]. Adding these exponents gives:

[tex]$$1 + 8 + 3 = 12$$[/tex]

3. Combine the product of the coefficients with the sum of the exponents on [tex]$x$[/tex] to get the final product:

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

Thus, the product is

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