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) \( \frac{a^{c}}{d+2} \)

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) \( \frac{a^{c}}{d + 2} = 9 \)