To simplify the expression [tex]\(\left(x^4\right)^9\)[/tex], you would use the power of a power law. Here's a detailed, step-by-step explanation of how it works:
1. Identify the structure of the expression: [tex]\(\left(x^4\right)^9\)[/tex]. This involves raising a power ([tex]\(x^4\)[/tex]) to another power (9).
2. Recall the power of a power law: When you raise a power to another power, you multiply the exponents. Mathematically, this can be expressed as [tex]\(\left(a^m\right)^n = a^{m \cdot n}\)[/tex].
3. Apply this law to the given expression:
[tex]\[
\left(x^4\right)^9 = x^{4 \cdot 9}
\][/tex]
4. Perform the multiplication of the exponents:
[tex]\[
4 \cdot 9 = 36
\][/tex]
5. Substitute the product back into the expression:
[tex]\[
x^{4 \cdot 9} = x^{36}
\][/tex]
So, the simplified form of [tex]\(\left(x^4\right)^9\)[/tex] is [tex]\(x^{36}\)[/tex].
