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Answer :
To find the product
[tex]$$
(4x)\left(-3x^8\right)\left(-7x^3\right),
$$[/tex]
we can use two important rules of algebra:
1. Multiply the coefficients.
2. When multiplying powers with the same base, add the exponents.
Step 1: Multiply the Coefficients
The coefficients are 4, -3, and -7. Multiply them as follows:
[tex]$$
4 \times (-3) = -12,
$$[/tex]
and then
[tex]$$
-12 \times (-7) = 84.
$$[/tex]
Step 2: Add the Exponents
The exponents for [tex]$x$[/tex] in each term are 1 (since [tex]$4x = 4x^1$[/tex]), 8, and 3. Add these exponents:
[tex]$$
1 + 8 + 3 = 12.
$$[/tex]
Final Answer
Combine the coefficient and the variable with its exponent:
[tex]$$
84x^{12}.
$$[/tex]
Thus, the product is [tex]$\boxed{84x^{12}}$[/tex].
[tex]$$
(4x)\left(-3x^8\right)\left(-7x^3\right),
$$[/tex]
we can use two important rules of algebra:
1. Multiply the coefficients.
2. When multiplying powers with the same base, add the exponents.
Step 1: Multiply the Coefficients
The coefficients are 4, -3, and -7. Multiply them as follows:
[tex]$$
4 \times (-3) = -12,
$$[/tex]
and then
[tex]$$
-12 \times (-7) = 84.
$$[/tex]
Step 2: Add the Exponents
The exponents for [tex]$x$[/tex] in each term are 1 (since [tex]$4x = 4x^1$[/tex]), 8, and 3. Add these exponents:
[tex]$$
1 + 8 + 3 = 12.
$$[/tex]
Final Answer
Combine the coefficient and the variable with its exponent:
[tex]$$
84x^{12}.
$$[/tex]
Thus, the product is [tex]$\boxed{84x^{12}}$[/tex].
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