Evaluate the surd expression: Compute (√13)^4 (write your answer as an integer).

Introduction / Context:This is a straightforward surds-and-indices computation. Recognize how exponents distribute over radicals and simplify to an integer using exponent rules. No approximation is required.

Given Data / Assumptions:

• Expression: (√13)^4.
• Use index and radical rules: √13 = 13^(1/2).

Concept / Approach:Convert the radical to an exponent, then multiply exponents: (a^(m))^(n) = a^(m n). This yields a power of 13 that is easy to evaluate exactly.

Step-by-Step Solution:

Verification / Alternative check:Square first, then square again: (√13)^2 = 13; 13^2 = 169. Same result.

Why Other Options Are Wrong:

• 520, 14280: Products unrelated to the correct exponent evaluation.
• 28561: That is 13^4; we have 13^2.
• 13: That equals (√13)^2, not to the 4th power.

Common Pitfalls:Forgetting that exponents multiply when raising a power to a power, or misreading the expression as √(13^4).

Final Answer:169