This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
1. Do the following with the aid of a calculator a) Step 1: Add the numbers. -81 + 0.79 = -80.21 The result is: -80.21 b) Step 1: Simplify the expression. Adding a negative number is equivalent to subtracting. 31 + (-16) = 31 - 16 Step 2: Perform the subtraction. 31 - 16 = 15 The result is: 15 2. Simplify 2.1) Step 1: Calculate 3 raised to the power of 4. 3^4 = 3 × 3 × 3 × 3 Step 2: Perform the multiplication. 3 × 3 = 9 9 × 3 = 27 27 × 3 = 81 The simplified value is: 81 2.2) Step 1: Calculate 1.2 raised to the power of 3. 1.2^3 = 1.2 × 1.2 × 1.2 Step 2: Perform the multiplication. 1.2 × 1.2 = 1.44 1.44 × 1.2 = 1.728 The simplified value is: 1.728 2.3) Step 1: Calculate 2.3 raised to the power of 1.75. 2.3^1.75 Using a calculator: 2.3^1.75 ≈ 4.4170 The simplified value (rounded to four decimal places) is: 4.4170 3. Use the calculator to calculate 3.1) Step 1: Calculate each term separately. First term: (62.4)^1.3 (62.4)^1.3 ≈ 251.3852 Second term: (173)/(85) (173)/(85) ≈ 2.0353 Third term: [4]898 [4]898 = 898^1/4 = 898^0.25 ≈ 5.4886 Step 2: Substitute these values back into the expression. (62.4)^1.3 + (173)/(85) - [4]898 ≈ 251.3852 + 2.0353 - 5.4886 Step 3: Perform the addition and subtraction. 251.3852 + 2.0353 = 253.4205 253.4205 - 5.4886 = 247.9319 The final calculated value (rounded to four decimal places) is: 247.9319