Combine exponents with a common base: If 10^(2/5) × 10^(8/5) = 10^n, determine the value of n.

Introduction / Context:
This quick test checks your fluency with adding exponents when multiplying like bases. The base 10 is common to both terms, so the product is another power of 10 with an exponent equal to the sum of the original exponents.

Given Data / Assumptions:

• Bases are the same: 10.
• Exponents: 2/5 and 8/5.
• Property: a^m * a^n = a^(m + n) for any real exponents m and n.

Concept / Approach:
Add the fractional exponents: 2/5 + 8/5 = 10/5. Then simplify the fraction to get an integer exponent. The result is a simple power of 10 that can be named or computed numerically if needed.

Step-by-Step Solution:

Verification / Alternative check:
Evaluate numerically: 10^(0.4) × 10^(1.6) = 10^(2.0) by exponent addition, confirming n = 2.

Why Other Options Are Wrong:
3, 4, 6, 10 reflect mis-additions or multiplications of exponents instead of addition.

Common Pitfalls:
Multiplying exponents (incorrect) instead of adding them when bases are equal.

Final Answer:
2