Math Problem Statement

Sederhanakan

Simplify the expression: (3^(n+1) - 3^n) / (3^n - 3^(n-1))

Solution

The given expression simplifies to 33.

Would you like further details on the simplification process, or do you have any other questions?

Here are five related questions for further practice:

  1. How can we factor expressions involving powers of 3?
  2. What would happen if the base in the given expression were 2 instead of 3?
  3. How does the exponent rule am/an=amna^m / a^n = a^{m-n} apply in this case?
  4. Can you generalize this type of simplification for any base, not just 3?
  5. What is the result if you evaluate the expression for a specific nn, like n=2n = 2?

Tip: When simplifying exponential expressions, always look for common factors in both the numerator and denominator to reduce the expression more easily.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Simplification of Algebraic Expressions

Formulas

a^m / a^n = a^(m-n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 9-12