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The evaluation of the expression is:

\[
\left( \frac{1}{8} \right)^{\frac{2}{3}} + \sin\left(\frac{11\pi}{3}\right) + 5 \cos\left(\frac{29\pi}{6}\right) = \frac{1}{4} - 3\sqrt{3}
\]

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Here are five related questions:
1. How do we simplify fractional exponents like \(\left(\frac{1}{8}\right)^{\frac{2}{3}}\)?
2. What are the sine and cosine values for angles greater than \(2\pi\) (e.g., \(\frac{11\pi}{3}\))?
3. Why does \(\cos\left(\frac{29\pi}{6}\right)\) result in a negative value?
4. What methods can we use to simplify trigonometric expressions without a calculator?
5. How are the sine and cosine values derived from the unit circle?

**Tip:** Remember that sine and cosine functions are periodic with a period of \(2\pi\), which helps simplify angles outside the usual interval \([0, 2\pi]\).

Evaluate (1/8)^(2/3) + sin(11π/3) + 5 cos(29π/6) without using a calculator.

This solution explains how to evaluate the expression (1/8)^(2/3) + sin(11π/3) + 5 cos(29π/6) without using a calculator. It covers exponent rules, trigonometric function periodicity, and simplifying angles in radians. Suitable for advanced high school or early college-level math students.

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