Answer :
To find the product [tex]\((4x)\left(-3x^8\right)\left(-7x^3\right)\)[/tex], let's break it down step-by-step:
1. Multiply the Coefficients:
- Start by multiplying the numerical coefficients:
- [tex]\(4 \times (-3) \times (-7)\)[/tex].
- First, [tex]\(4 \times (-3) = -12\)[/tex].
- Then, [tex]\(-12 \times (-7) = 84\)[/tex].
2. Add the Exponents:
- Next, we handle the exponents of [tex]\(x\)[/tex].
- In [tex]\(4x\)[/tex], the exponent is 1.
- In [tex]\(-3x^8\)[/tex], the exponent is 8.
- In [tex]\(-7x^3\)[/tex], the exponent is 3.
- Add the exponents together: [tex]\(1 + 8 + 3 = 12\)[/tex].
3. Combine the Results:
- Now, combine the product of the coefficients and the sum of the exponents to get the final expression.
- The product is [tex]\(84\)[/tex] and the total exponent is [tex]\(12\)[/tex].
Therefore, the product of the expression is [tex]\(84x^{12}\)[/tex].
The correct answer is [tex]\(84x^{12}\)[/tex].
1. Multiply the Coefficients:
- Start by multiplying the numerical coefficients:
- [tex]\(4 \times (-3) \times (-7)\)[/tex].
- First, [tex]\(4 \times (-3) = -12\)[/tex].
- Then, [tex]\(-12 \times (-7) = 84\)[/tex].
2. Add the Exponents:
- Next, we handle the exponents of [tex]\(x\)[/tex].
- In [tex]\(4x\)[/tex], the exponent is 1.
- In [tex]\(-3x^8\)[/tex], the exponent is 8.
- In [tex]\(-7x^3\)[/tex], the exponent is 3.
- Add the exponents together: [tex]\(1 + 8 + 3 = 12\)[/tex].
3. Combine the Results:
- Now, combine the product of the coefficients and the sum of the exponents to get the final expression.
- The product is [tex]\(84\)[/tex] and the total exponent is [tex]\(12\)[/tex].
Therefore, the product of the expression is [tex]\(84x^{12}\)[/tex].
The correct answer is [tex]\(84x^{12}\)[/tex].
