Certainly! Let's simplify the expression [tex]\(\left(x^{a+b}\right)^{a-b}\)[/tex].
Step-by-Step Solution:
1. Understand the expression: We start with [tex]\(\left(x^{a+b}\right)^{a-b}\)[/tex].
2. Apply the power-of-a-power rule: The rule states that [tex]\((x^m)^n = x^{m \cdot n}\)[/tex]. In our case, [tex]\(m = a+b\)[/tex] and [tex]\(n = a-b\)[/tex].
3. Simplify the exponents:
[tex]\[
\left(x^{a+b}\right)^{a-b} = x^{(a+b) \cdot (a-b)}
\][/tex]
Thus, the simplified form of the expression [tex]\(\left(x^{a+b}\right)^{a-b}\)[/tex] remains [tex]\(\boxed{\left(x^{a+b}\right)^{a-b}}\)[/tex].
