To solve the expression [tex]\(\left(c^4\right)^3\)[/tex], we need to use the power of a power rule in exponents. The power of a power rule states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. Here is a step-by-step solution:
1. Identify the base and the exponents in the expression [tex]\(\left(c^4\right)^3\)[/tex].
- The base is [tex]\(c\)[/tex].
- The exponent inside the parentheses is 4.
- The exponent outside the parentheses is 3.
2. Apply the power of a power rule:
[tex]\[
\left(c^4\right)^3 = c^{4 \cdot 3}
\][/tex]
3. Multiply the exponents together:
[tex]\[
4 \cdot 3 = 12
\][/tex]
4. Write the simplified expression:
[tex]\[
c^{12}
\][/tex]
With these steps, we have simplified the expression [tex]\(\left(c^4\right)^3\)[/tex] to [tex]\(c^{12}\)[/tex].
Therefore, the correct answer is [tex]\(c^{12}\)[/tex].
