a. \( \left(6^{2} \div 6 \times 4\right) \div\left(2^{2}+2\right)= \) b. \( (72 \div 9 \div 2)^{2}+\left(9^{0}+2^{2}\right) \)

**a. Evaluating** \( \left(6^{2} \div 6 \times 4\right) \div\left(2^{2}+2\right) \) 1. Compute the exponent: \[ 6^{2} = 36 \] 2. Evaluate the numerator expression from left to right (division and multiplication have the same precedence): \[ 36 \div 6 = 6 \quad \text{and then} \quad 6 \times 4 = 24 \] 3. Evaluate the denominator: \[ 2^{2} = 4 \quad \text{so} \quad 4 + 2 = 6 \] 4. Divide the results: \[ 24 \div 6 = 4 \] Thus, the answer for part (a) is \(4\). --- **b. Evaluating** \( (72 \div 9 \div 2)^{2}+\left(9^{0}+2^{2}\right) \) 1. Evaluate the expression inside the parentheses in the first term: - Divide from left to right: \[ 72 \div 9 = 8 \quad \text{and then} \quad 8 \div 2 = 4 \] 2. Square the result: \[ 4^{2} = 16 \] 3. Evaluate the expression inside the second set of parentheses: - Any non-zero number raised to the power of 0 equals 1: \[ 9^{0} = 1 \] - Compute: \[ 2^{2} = 4 \] - Sum the two: \[ 1 + 4 = 5 \] 4. Sum the two parts together: \[ 16 + 5 = 21 \] Thus, the answer for part (b) is \(21\).