Answer :
We are given the expression:
[tex]$$
(4x) \cdot (-3x^8) \cdot (-7x^3).
$$[/tex]
Step 1: Multiply the coefficients
Multiply the numbers (coefficients) together:
[tex]$$
4 \times (-3) \times (-7).
$$[/tex]
First, [tex]$4 \times (-3) = -12$[/tex]. Then,
[tex]$$
-12 \times (-7) = 84.
$$[/tex]
Step 2: Multiply the powers of [tex]$x$[/tex]
For the variable part, use the rule:
[tex]$$
x^a \cdot x^b = x^{a+b}.
$$[/tex]
In our expression, the exponents are:
- For [tex]$4x$[/tex], the exponent is [tex]$1$[/tex].
- For [tex]$-3x^8$[/tex], the exponent is [tex]$8$[/tex].
- For [tex]$-7x^3$[/tex], the exponent is [tex]$3$[/tex].
Add the exponents:
[tex]$$
1 + 8 + 3 = 12.
$$[/tex]
Thus, the product for the variable part is:
[tex]$$
x^{12}.
$$[/tex]
Step 3: Combine the results
The final product is the product of the coefficients and the variable part:
[tex]$$
84 \cdot x^{12}.
$$[/tex]
So the final answer is:
[tex]$$
\boxed{84x^{12}}.
$$[/tex]
[tex]$$
(4x) \cdot (-3x^8) \cdot (-7x^3).
$$[/tex]
Step 1: Multiply the coefficients
Multiply the numbers (coefficients) together:
[tex]$$
4 \times (-3) \times (-7).
$$[/tex]
First, [tex]$4 \times (-3) = -12$[/tex]. Then,
[tex]$$
-12 \times (-7) = 84.
$$[/tex]
Step 2: Multiply the powers of [tex]$x$[/tex]
For the variable part, use the rule:
[tex]$$
x^a \cdot x^b = x^{a+b}.
$$[/tex]
In our expression, the exponents are:
- For [tex]$4x$[/tex], the exponent is [tex]$1$[/tex].
- For [tex]$-3x^8$[/tex], the exponent is [tex]$8$[/tex].
- For [tex]$-7x^3$[/tex], the exponent is [tex]$3$[/tex].
Add the exponents:
[tex]$$
1 + 8 + 3 = 12.
$$[/tex]
Thus, the product for the variable part is:
[tex]$$
x^{12}.
$$[/tex]
Step 3: Combine the results
The final product is the product of the coefficients and the variable part:
[tex]$$
84 \cdot x^{12}.
$$[/tex]
So the final answer is:
[tex]$$
\boxed{84x^{12}}.
$$[/tex]
