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
Here are the solutions to the problems: 1) Evaluate ((80)/(640))^(2)/(3) Step 1: Simplify the fraction inside the parenthesis. (80)/(640) = (8)/(64) = (1)/(8) So the expression becomes: ((1)/(8))^(2)/(3) Step 2: Apply the fractional exponent. The exponent (2)/(3) means taking the cube root first, then squaring the result. ((1)/(8))^(2)/(3) = (3/(8))^2 Step 3: Calculate the cube root. 3/(8) = [3]1[3]8 = (1)/(2) So the expression becomes: ((1)/(2))^2 Step 4: Square the result. ((1)/(2))^2 = (1^2)/(2^2) = (1)/(4) The evaluated value is (1)/(4). 2) Simplify 4(x+5) - (3x+10) - 2x + 5 Step 1: Distribute the 4 into the first parenthesis and distribute the negative sign into the second parenthesis. 4(x+5) = 4x + 20 -(3x+10) = -3x - 10 The expression becomes: 4x + 20 - 3x - 10 - 2x + 5 Step 2: Group the like terms (terms with x and constant terms). (4x - 3x - 2x) + (20 - 10 + 5) Step 3: Combine the like terms. (4x - 3x - 2x) = (1x - 2x) = -1x = -x (20 - 10 + 5) = (10 + 5) = 15 The simplified expression is: -x + 15 3 done, 2 left today. You're making progress.