(9) \( -s^{3}-5 s t \) when \( s=-3 \) and \( t=-2 \) (10) \( \frac{a^{2}-b^{2}}{a-b} \) when \( a=5 \) and \( b=-9 \) when \( g=2, h=-3 \), and \( w=-7 \) \( g^{2}-3(h-g)-w^{2} \) (12) \( r^{3}-\left[q+(r-s)^{2}\right] \) when \( r=3, q=2 \), and \( s=5 \)

Sure, let's evaluate each of the given expressions with the specified values step by step. --- ### Problem (9) \[ -s^{3} - 5 s t \] **Given:** \( s = -3 \), \( t = -2 \) **Step-by-Step Evaluation:** 1. **Calculate \( s^{3} \):** \[ s^{3} = (-3)^{3} = -27 \] 2. **Calculate \( 5 s t \):** \[ 5 s t = 5 \times (-3) \times (-2) = 5 \times 6 = 30 \] 3. **Combine the results:** \[ -s^{3} - 5 s t = -(-27) - 30 = 27 - 30 = -3 \] **Answer:** \(-3\) --- ### Problem (10) \[ \frac{a^{2} - b^{2}}{a - b} \] **Given:** \( a = 5 \), \( b = -9 \) **Step-by-Step Evaluation:** 1. **Calculate \( a^{2} \) and \( b^{2} \):** \[ a^{2} = 5^{2} = 25 \] \[ b^{2} = (-9)^{2} = 81 \] 2. **Compute the numerator \( a^{2} - b^{2} \):** \[ a^{2} - b^{2} = 25 - 81 = -56 \] 3. **Compute the denominator \( a - b \):** \[ a - b = 5 - (-9) = 5 + 9 = 14 \] 4. **Divide the numerator by the denominator:** \[ \frac{a^{2} - b^{2}}{a - b} = \frac{-56}{14} = -4 \] **Answer:** \(-4\) --- ### Problem (11) \[ g^{2} - 3(h - g) - w^{2} \] **Given:** \( g = 2 \), \( h = -3 \), \( w = -7 \) **Step-by-Step Evaluation:** 1. **Calculate \( g^{2} \) and \( w^{2} \):** \[ g^{2} = 2^{2} = 4 \] \[ w^{2} = (-7)^{2} = 49 \] 2. **Calculate \( h - g \):** \[ h - g = -3 - 2 = -5 \] 3. **Multiply by 3:** \[ 3(h - g) = 3 \times (-5) = -15 \] 4. **Combine all parts:** \[ g^{2} - 3(h - g) - w^{2} = 4 - (-15) - 49 = 4 + 15 - 49 = 19 - 49 = -30 \] **Answer:** \(-30\) --- ### Problem (12) \[ r^{3} - \left[ q + (r - s)^{2} \right] \] **Given:** \( r = 3 \), \( q = 2 \), \( s = 5 \) **Step-by-Step Evaluation:** 1. **Calculate \( r^{3} \):** \[ r^{3} = 3^{3} = 27 \] 2. **Calculate \( r - s \):** \[ r - s = 3 - 5 = -2 \] 3. **Calculate \( (r - s)^{2} \):** \[ (r - s)^{2} = (-2)^{2} = 4 \] 4. **Compute the expression inside the brackets:** \[ q + (r - s)^{2} = 2 + 4 = 6 \] 5. **Subtract the bracketed term from \( r^{3} \):** \[ r^{3} - [q + (r - s)^{2}] = 27 - 6 = 21 \] **Answer:** \(21\) --- ### Summary of Answers 1. **Problem (9):** \(-3\) 2. **Problem (10):** \(-4\) 3. **Problem (11):** \(-30\) 4. **Problem (12):** \(21\) If you have any further questions or need more explanations, feel free to ask!