To address the expression [tex]\(\left(1 - \frac{2}{3x}\right)^5\)[/tex], we will follow these steps:
1. Identify the components:
- The base of the expression is [tex]\( \left(1 - \frac{2}{3x}\right) \)[/tex].
- The exponent is [tex]\( 5 \)[/tex].
2. Combine the terms inside the parentheses:
- Within the parentheses, you have [tex]\( 1 \)[/tex] and [tex]\( \frac{2}{3x} \)[/tex].
3. Recap and rewrite:
- The expression inside the parentheses, [tex]\(1 - \frac{2}{3x}\)[/tex], is a difference where [tex]\(1\)[/tex] is subtracted by [tex]\(\frac{2}{3x}\)[/tex].
4. Raise the simplified base to the power:
- The resulting base [tex]\( \left(1 - \frac{2}{3x}\right) \)[/tex] is then raised to the power [tex]\( 5 \)[/tex].
Therefore, the step-by-step process confirms that the expression [tex]\(\left(1 - \frac{2}{3x}\right)^5\)[/tex] is already in its simplest form and cannot be simplified further without additional context or values for [tex]\( x \)[/tex]. The completed and simplified expression is:
[tex]\[
\boxed{\left(1 - \frac{2}{3x}\right)^5}
\][/tex]
