9) \( -2 x^{\frac{5}{3}}-3=-489 \)

Let’s solve for \( x \) in the equation \( -2 x^{\frac{5}{3}} - 3 = -489 \). First, add 3 to both sides: \[ -2 x^{\frac{5}{3}} = -486 \] Next, divide by -2: \[ x^{\frac{5}{3}} = 243 \] Now, to eliminate the fractional exponent, raise both sides to the reciprocal, which is \( \frac{3}{5} \): \[ x = 243^{\frac{3}{5}} \] Calculating \( 243^{\frac{1}{5}} \) gives \( 3 \) because \( 3^5 = 243 \). So now we have: \[ x = 3^3 = 27 \] Thus, the solution to the equation is \( x = 27 \).