The expression you have provided is \(\left(2x - 13\right)^{n+1}\), which is a binomial expression raised to the power of \(n+1\).

Here are a few common ways to deal with this expression depending on the context:

### 1. **Expand using Binomial Theorem (for small values of \(n+1\)):**
If \(n+1\) is a small integer, we can expand \(\left(2x - 13\right)^{n+1}\) using the binomial theorem:
\[
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
\]
where \(a = 2x\), \(b = -13\), and \(n = n+1\).

### 2. **Simplify or evaluate for specific values of \(n+1\):**
If you know the value of \(n\), you can substitute it and simplify.

### 3. **Take derivatives or integrals:**
You could differentiate or integrate this expression with respect to \(x\) depending on the context.

Do you need a specific operation performed on this expression (e.g., expansion, differentiation, etc.)?

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Here are five questions you could explore next:
1. Would you like to expand this expression for a particular value of \(n\)?
2. Do you need to find the derivative of this expression?
3. Would you like to see how to integrate this expression?
4. Do you need a specific numerical evaluation for some value of \(x\) and \(n\)?
5. Are you interested in solving an equation involving this expression?

**Tip**: The binomial theorem is especially useful for expanding powers of binomials when dealing with integer exponents.

Explore the binomial expansion of the expression (2x - 13)^(n+1) using the binomial theorem. Learn key concepts in algebra, exponents, and binomial expansion with a step-by-step guide for students in Grades 11-12.

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