Solve an exponential equation and evaluate x^x: If 3^x − 3^(x−1) = 18, find the value of x^x.

Introduction / Context:
The equation features the same base 3 raised to related exponents. Factoring out the common term 3^(x−1) reduces it to a simple linear equation in the exponent. Then evaluate x^x using the obtained integer x.

Given Data / Assumptions:

• 3^x − 3^(x−1) = 18.
• Compute x^x after solving x.

Concept / Approach:
Use 3^x = 3 * 3^(x−1). Then the left side becomes (3 − 1)*3^(x−1) = 2*3^(x−1), which is easy to solve.

Step-by-Step Solution:

Verification / Alternative check:
Substitute x = 3 into the original: 27 − 9 = 18, correct.

Why Other Options Are Wrong:

• 3, 8, 216: These correspond to 3^1, 2^3, and 6^3—unrelated to x^x with x = 3.

Common Pitfalls:
Not factoring out 3^(x−1) or misapplying exponent subtraction.

Final Answer: