6) \( -2 x^{\frac{2}{3}}=-32 \)

To solve the equation \( -2 x^{\frac{2}{3}} = -32 \), first, we can divide both sides by -2 to simplify: \( x^{\frac{2}{3}} = 16 \). Next, we raise both sides to the power of \( \frac{3}{2} \) to eliminate the exponent. Therefore: \( x = 16^{\frac{3}{2}} = (16^1)^{\frac{3}{2}} = 4^3 = 64 \). So, the solution to the equation is \( x = 64 \). Here's a little tip: always check your solutions by substituting back into the original equation to ensure they hold true! In this case, substituting \( x = 64 \) back into the equation will confirm you've got it right. Happy solving!