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 :

Let's solve the expression step-by-step:

Given expression: [tex]\((4x)(-3x^8)(-7x^3)\)[/tex]

1. Multiply the Coefficients:

The coefficients are 4, -3, and -7. Multiply them together:

[tex]\(4 \times (-3) = -12\)[/tex]
[tex]\(-12 \times (-7) = 84\)[/tex]

So, the product of the coefficients is 84.

2. Add the Exponents:

The exponents of [tex]\(x\)[/tex] are 1 (since [tex]\(4x = 4x^1\)[/tex]), 8, and 3. Add these exponents:

[tex]\(1 + 8 + 3 = 12\)[/tex]

So, the sum of the exponents is 12.

3. Combine Coefficient and Exponent:

The product is:

[tex]\(84x^{12}\)[/tex]

Therefore, the correct answer is [tex]\(84x^{12}\)[/tex].

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