College

What is the product?

[tex] (4x)\left(-3x^6\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 problem step by step:

We need to find the product of the expression:

[tex]\[
(4x)(-3x^6)(-7x^3)
\][/tex]

Step 1: Multiply the numerical coefficients.

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

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

Step 2: Multiply the powers of [tex]\(x\)[/tex].

Each term in the product has a power of [tex]\(x\)[/tex]. We add these exponents together:

- The first term, [tex]\(4x\)[/tex], has an exponent of 1.
- The second term, [tex]\(-3x^6\)[/tex], has an exponent of 6.
- The third term, [tex]\(-7x^3\)[/tex], has an exponent of 3.

Add these exponents:

[tex]\[
1 + 6 + 3 = 10
\][/tex]

Step 3: Combine the results.

Combine the results from Steps 1 and 2 to get the final product:

The coefficient is 84, and the power of [tex]\(x\)[/tex] is 10. Therefore, the product is:

[tex]\[
84x^{10}
\][/tex]

The correct answer from the given choices should be: [tex]\(84x^{10}\)[/tex]. However, none of the options provided directly match this expression, so there might be an issue with the provided options.