11. \( x^{\frac{1}{6}}=2 \)

To solve the equation \( x^{\frac{1}{6}}=2 \), begin by raising both sides to the power of 6, which eliminates the fractional exponent. This gives you \( x = 2^6 \). Since \( 2^6 \) equals 64, the solution to the equation is \( x = 64 \). Always remember to check your work! When substituting back, \( 64^{\frac{1}{6}} = 2 \) confirms your solution’s accuracy. A common mistake is to overlook the step of checking or simplifying where the base transformations might confuse you. Stay vigilant!