Question 1 If $$ a=3, b=-3, c=4 $$ and $$ d=7 $$, evaluate: a) $$ \frac{4 a-2}{c} $$ b) $$ \frac{b^{2}+b^{3}}{a-c} $$ c) $$ \frac{a^{c}}{d+2} $$

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Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(4\times 3-2\right)}{4}$$
- step1: Remove the parentheses:
  $$\frac{4\times 3-2}{4}$$
- step2: Multiply the numbers:
  $$\frac{12-2}{4}$$
- step3: Subtract the numbers:
  $$\frac{10}{4}$$
- step4: Reduce the fraction:
  $$\frac{5}{2}$$
Calculate or simplify the expression $$ ((-3)^2+(-3)^3)/(3-4) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(\left(-3\right)^{2}+\left(-3\right)^{3}\right)}{\left(3-4\right)}$$
- step1: Remove the parentheses:
  $$\frac{\left(-3\right)^{2}+\left(-3\right)^{3}}{3-4}$$
- step2: Subtract the numbers:
  $$\frac{-18}{3-4}$$
- step3: Subtract the numbers:
  $$\frac{-18}{-1}$$
- step4: Divide the terms:
  $$18$$
Calculate or simplify the expression $$ (3^4)/(7+2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{3^{4}}{\left(7+2\right)}$$
- step1: Remove the parentheses:
  $$\frac{3^{4}}{7+2}$$
- step2: Add the numbers:
  $$\frac{3^{4}}{9}$$
- step3: Rewrite the expression:
  $$\frac{3^{4}}{3^{2}}$$
- step4: Divide the numbers:
  $$3^{4-2}$$
- step5: Subtract the terms:
  $$3^{2}$$
- step6: Evaluate the power:
  $$9$$
Let's evaluate each expression step by step using the given values $$ a=3, b=-3, c=4, d=7 $$.

### a) Evaluate $$ \frac{4a - 2}{c} $$

1. Substitute the values:
   $$
   \frac{4 \cdot 3 - 2}{4}
   $$
2. Calculate the numerator:
   $$
   4 \cdot 3 = 12 \quad \Rightarrow \quad 12 - 2 = 10
   $$
3. Now, divide by $$ c $$:
   $$
   \frac{10}{4} = \frac{5}{2} = 2.5
   $$

### b) Evaluate $$ \frac{b^{2} + b^{3}}{a - c} $$

1. Substitute the values:
   $$
   \frac{(-3)^{2} + (-3)^{3}}{3 - 4}
   $$
2. Calculate $$ b^2 $$ and $$ b^3 $$:
   $$
   (-3)^{2} = 9 \quad \text{and} \quad (-3)^{3} = -27
   $$
3. Now, calculate the numerator:
   $$
   9 + (-27) = 9 - 27 = -18
   $$
4. Calculate the denominator:
   $$
   3 - 4 = -1
   $$
5. Now, divide:
   $$
   \frac{-18}{-1} = 18
   $$

### c) Evaluate $$ \frac{a^{c}}{d + 2} $$

1. Substitute the values:
   $$
   \frac{3^{4}}{7 + 2}
   $$
2. Calculate $$ 3^{4} $$:
   $$
   3^{4} = 81
   $$
3. Calculate the denominator:
   $$
   7 + 2 = 9
   $$
4. Now, divide:
   $$
   \frac{81}{9} = 9
   $$

### Final Results
- a) $$ \frac{4a - 2}{c} = 2.5 $$
- b) $$ \frac{b^{2} + b^{3}}{a - c} = 18 $$
- c) $$ \frac{a^{c}}{d + 2} = 9 $$
a) 2.5 b) 18 c) 9

Question 1 If \( a=3, b=-3, c=4 \) and \( d=7 \), evaluate: a) \( \frac{4 a-2}{c} \) b) \( \frac{b^{2}+b^{3}}{a-c} \) c) \( \frac{a^{c}}{d+2} \)

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