To simplify the expression [tex]\(\left(x^4\right)^9\)[/tex], we use the "power of a power" law in exponents. The "power of a power" law states that when raising an exponent to another exponent, you multiply the exponents.
Here's the step-by-step solution:
1. Start with the expression: [tex]\(\left(x^4\right)^9\)[/tex].
2. Apply the "power of a power" law, which tells us that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. In our case, [tex]\(a = x\)[/tex], [tex]\(m = 4\)[/tex], and [tex]\(n = 9\)[/tex].
3. Multiply the exponents [tex]\(4\)[/tex] and [tex]\(9\)[/tex]:
[tex]\[
4 \times 9 = 36
\][/tex]
4. Therefore, [tex]\(\left(x^4\right)^9\)[/tex] simplifies to:
[tex]\[
x^{36}
\][/tex]
So, the correct law to use for this problem is the "power of a power" law, and the simplified form of the given expression is [tex]\(x^{36}\)[/tex].
