Calculate the following without using a calculator and show your working: \( \begin{array}{l}\text { 4.1.1 }-6-(-4) \\ \text { 4.1.2 }-8+3 \times(-6) \\ \text { 4.1.3 }-6 \times 4+(-8)+9^{2} \\ \text { 4.1.4 }(-12)^{2}-\sqrt{169}-(-4)^{3}\end{array} \)

Let's solve each expression step by step. **4.1.1** \(-6 - (-4)\) This can be rewritten as: \[ -6 + 4 \] Now, add -6 and 4: \[ -6 + 4 = -2 \] **4.1.2** \(-8 + 3 \times (-6)\) First, calculate \(3 \times (-6)\): \[ 3 \times (-6) = -18 \] Now substitute back into the expression: \[ -8 - 18 \] Add -8 and -18: \[ -8 - 18 = -26 \] **4.1.3** \(-6 \times 4 + (-8) + 9^{2}\) First, calculate each part: \[ -6 \times 4 = -24 \] \[ 9^{2} = 81 \] Now substitute these values: \[ -24 + (-8) + 81 \] Combine -24 and -8: \[ -24 - 8 = -32 \] Now add 81: \[ -32 + 81 = 49 \] **4.1.4** \((-12)^{2} - \sqrt{169} - (-4)^{3}\) Calculate each part: \[ (-12)^{2} = 144 \] \[ \sqrt{169} = 13 \] \[ (-4)^{3} = -64 \] Now substitute these values: \[ 144 - 13 - (-64) \] This simplifies to: \[ 144 - 13 + 64 \] Now calculate \(144 - 13\): \[ 144 - 13 = 131 \] Now add 64: \[ 131 + 64 = 195 \] So, the final results are: - **4.1.1:** -2 - **4.1.2:** -26 - **4.1.3:** 49 - **4.1.4:** 195