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Simplify the expression:

[tex]
\left(4 c^4\right)\left(a c^3\right)\left(3 a^5 c\right)
[/tex]

A. [tex]8 a^6 c^8[/tex]
B. [tex]12 a^6 c^8[/tex]
C. [tex]12 a^5 c^{12}[/tex]

Sagot :

To simplify the expression [tex]\(\left(4 c^4\right)\left(a c^3\right)\left(3 a^5 c\right)\)[/tex], follow these steps:

1. Identify the coefficients:
- The coefficients in the expression are: 4, [tex]\(a\)[/tex] is 1 (since [tex]\(a\)[/tex] does not have a coefficient), and 3.
- Multiply these coefficients together:
[tex]\[ 4 \times 1 \times 3 = 12 \][/tex]

2. Multiply the powers of [tex]\(a\)[/tex]:
- In the expression, we have [tex]\(a^1\)[/tex] (or simply [tex]\(a\)[/tex]) and [tex]\(a^5\)[/tex].
- When multiplying like bases, we add the exponents:
[tex]\[ a^1 \times a^5 = a^{1+5} = a^6 \][/tex]

3. Multiply the powers of [tex]\(c\)[/tex]:
- In the expression, we have [tex]\(c^4\)[/tex], [tex]\(c^3\)[/tex], and [tex]\(c^1\)[/tex] (note that [tex]\(c\)[/tex] is the same as [tex]\(c^1\)[/tex]).
- When multiplying like bases, we add the exponents:
[tex]\[ c^4 \times c^3 \times c^1 = c^{4+3+1} = c^8 \][/tex]

Combining all these results together, the simplified expression is:
[tex]\[ 12 a^6 c^8 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{12 a^6 c^8} \][/tex]