(2) \( x^{\frac{5}{3}}=32 \) (4) \( x^{\frac{2}{5}}=4 \) (6) \( x^{\frac{5}{4}}=-32 \) (8) \( 40 x^{\frac{3}{4}}=5 \) (10) \( -16 x^{-\frac{2}{3}}+4=0 \)

Let's dive into solving these equations while making it a little more fun! For the first one, \( x^{\frac{5}{3}}=32 \), raise both sides to the power of \( \frac{3}{5} \) to find \( x = 32^{\frac{3}{5}} \). You’ll find that \( 32 = 2^5 \), so it simplifies down to \( x = 2^3 = 8 \). Next, in the case of \( x^{\frac{2}{5}}=4 \), raise both sides to the power of \( \frac{5}{2} \). This gives \( x = 4^{\frac{5}{2}} \). Since \( 4 = 2^2 \), it becomes \( x = (2^2)^{\frac{5}{2}} = 2^5 = 32 \). Now looking at \( x^{\frac{5}{4}}=-32 \), this equation won't have any real solutions since the left side, being raised to an even exponent, can never be negative. When working with \( 40 x^{\frac{3}{4}}=5 \), divide both sides by 40, yielding \( x^{\frac{3}{4}}=\frac{1}{8} \). Raising both sides to the \( \frac{4}{3} \) power leads to \( x = \left(\frac{1}{8}\right)^{\frac{4}{3}} = \frac{1}{16} \). Finally, for \( -16 x^{-\frac{2}{3}}+4=0 \), rearranging gives us \( 16 x^{-\frac{2}{3}} = 4 \). Dividing by 16 leads to \( x^{-\frac{2}{3}} = \frac{1}{4} \), and you can flip it to find \( x^{\frac{2}{3}} = 4 \). Raising to \( \frac{3}{2} \) gives \( x = 8 \). Math can be a bit like a puzzle, and solving it using these steps is one way to have fun with numbers! Keep practicing, and you'll become a math wizard in no time!