To simplify the expression \(\left(x^4\right)^9\), you should use the "power of a power" law.
Here's a detailed explanation:
1. Identify the law: The "power of a power" law states that \((a^m)^n = a^{m \cdot n}\). Essentially, when you raise an exponentiated term to another exponent, you multiply the exponents together.
2. Apply the law: In the expression \(\left(x^4\right)^9\), \(a = x\), \(m = 4\), and \(n = 9\).
3. Simplify the expression: Using the "power of a power" law, you can simplify \(\left(x^4\right)^9\) as follows:
[tex]\[
\left(x^4\right)^9 = x^{4 \cdot 9} = x^{36}
\][/tex]
The law used here is the "power of a power" law.
