Find all real solutions. \( x^{2 / 9}=2 \)

To solve the equation \( x^{2 / 9} = 2 \), start by raising both sides to the power of \( \frac{9}{2} \) to eliminate the fractional exponent. This gives you \( x = 2^{\frac{9}{2}} \), simplifying to \( x = 2^4 \sqrt{2} = 16 \sqrt{2} \). Thus, the real solution is \( x = 16\sqrt{2} \). However, don't forget to check if there are any negative solutions, as fractional exponents can sometimes lead to various types of roots. In this case, since we're taking an even root (the denominator is 9), \( x \) must be non-negative, confirming that \( x = 16\sqrt{2} \) is indeed the only solution.