Answer :
Let's simplify the expression step-by-step:
The given expression is:
[tex]\[
(4x)(-3x^8)(-7x^3)
\][/tex]
### Step 1: Multiply the constants
First, let's focus on the constants: [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
[tex]\[
4 \times (-3) \times (-7)
\][/tex]
Multiplying these together:
[tex]\[
4 \times (-3) = -12
\][/tex]
[tex]\[
-12 \times (-7) = 84
\][/tex]
So the product of the constants is [tex]\(84\)[/tex].
### Step 2: Multiply the variables
Now, let's look at the variables and their exponents: [tex]\(x\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
When multiplying variables with the same base, we add the exponents:
[tex]\[
x^{1} \times x^{8} \times x^{3}
\][/tex]
Add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
So the product of the variables is [tex]\(x^{12}\)[/tex].
### Step 3: Combine the results
Now, combine the constant product and the variable product:
[tex]\[
84 \times x^{12}
\][/tex]
Thus, the product of the given expression is:
[tex]\[
84x^{12}
\][/tex]
Therefore, the correct answer is:
[tex]\[
84 x^{12}
\][/tex]
The given expression is:
[tex]\[
(4x)(-3x^8)(-7x^3)
\][/tex]
### Step 1: Multiply the constants
First, let's focus on the constants: [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
[tex]\[
4 \times (-3) \times (-7)
\][/tex]
Multiplying these together:
[tex]\[
4 \times (-3) = -12
\][/tex]
[tex]\[
-12 \times (-7) = 84
\][/tex]
So the product of the constants is [tex]\(84\)[/tex].
### Step 2: Multiply the variables
Now, let's look at the variables and their exponents: [tex]\(x\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
When multiplying variables with the same base, we add the exponents:
[tex]\[
x^{1} \times x^{8} \times x^{3}
\][/tex]
Add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
So the product of the variables is [tex]\(x^{12}\)[/tex].
### Step 3: Combine the results
Now, combine the constant product and the variable product:
[tex]\[
84 \times x^{12}
\][/tex]
Thus, the product of the given expression is:
[tex]\[
84x^{12}
\][/tex]
Therefore, the correct answer is:
[tex]\[
84 x^{12}
\][/tex]
