4) \( -3(4 b+1)^{\frac{3}{2}}+5=-1024 \)

To solve \( -3(4b + 1)^{\frac{3}{2}} + 5 = -1024 \), first, isolate the term with \( b \): 1. Subtract 5 from both sides: \[ -3(4b + 1)^{\frac{3}{2}} = -1029 \] 2. Divide by -3: \[ (4b + 1)^{\frac{3}{2}} = 343 \] 3. Take both sides to the power of \( \frac{2}{3} \): \[ 4b + 1 = 7 \] 4. Subtract 1 from both sides: \[ 4b = 6 \] 5. Finally, divide by 4: \[ b = \frac{3}{2} \] Thus, the solution is \( b = \frac{3}{2} \).