Answer :
To solve the given expression [tex]\((a^3 b^{12} c^2) \times (a^5 c^2) \times (b^5 c^4)^0\)[/tex], we need to simplify it step by step.
1. Handle the exponent of zero:
[tex]\((b^5 c^4)^0\)[/tex] simplifies to 1 because any expression raised to the power of 0 is 1.
So, the expression simplifies to:
[tex]\[ (a^3 b^{12} c^2) \times (a^5 c^2) \times 1 \][/tex]
The multiplication by 1 does not change the value, so it simplifies further to:
[tex]\[ (a^3 b^{12} c^2) \times (a^5 c^2) \][/tex]
2. Combine the like terms:
- For the [tex]\(a\)[/tex] terms:
[tex]\[ a^3 \times a^5 = a^{3+5} = a^8 \][/tex]
- For the [tex]\(b\)[/tex] terms:
[tex]\[ b^{12} \quad (\text{There are no other \(b\) terms to combine with}) \][/tex]
- For the [tex]\(c\)[/tex] terms:
[tex]\[ c^2 \times c^2 = c^{2+2} = c^4 \][/tex]
Thus, the simplified expression is:
[tex]\[ a^8 b^{12} c^4 \][/tex]
Therefore, the correct option is:
B. [tex]\(\mathbf{a^8 b^{12} c^4}\)[/tex]
1. Handle the exponent of zero:
[tex]\((b^5 c^4)^0\)[/tex] simplifies to 1 because any expression raised to the power of 0 is 1.
So, the expression simplifies to:
[tex]\[ (a^3 b^{12} c^2) \times (a^5 c^2) \times 1 \][/tex]
The multiplication by 1 does not change the value, so it simplifies further to:
[tex]\[ (a^3 b^{12} c^2) \times (a^5 c^2) \][/tex]
2. Combine the like terms:
- For the [tex]\(a\)[/tex] terms:
[tex]\[ a^3 \times a^5 = a^{3+5} = a^8 \][/tex]
- For the [tex]\(b\)[/tex] terms:
[tex]\[ b^{12} \quad (\text{There are no other \(b\) terms to combine with}) \][/tex]
- For the [tex]\(c\)[/tex] terms:
[tex]\[ c^2 \times c^2 = c^{2+2} = c^4 \][/tex]
Thus, the simplified expression is:
[tex]\[ a^8 b^{12} c^4 \][/tex]
Therefore, the correct option is:
B. [tex]\(\mathbf{a^8 b^{12} c^4}\)[/tex]
