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
I see the question asks to evaluate ((80)/(640))^-(2)/(3). Let's solve it with the negative exponent as shown in the printed question. 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 negative exponent rule. A negative exponent means taking the reciprocal of the base. ((1)/(8))^-(2)/(3) = ((8)/(1))^(2)/(3) = 8^(2)/(3) Step 3: Apply the fractional exponent. The exponent (2)/(3) means taking the cube root first, then squaring the result. 8^(2)/(3) = ([3]8)^2 Step 4: Calculate the cube root. [3]8 = 2 So the expression becomes: (2)^2 Step 5: Square the result. (2)^2 = 4 The evaluated value is 4. What's next? Send 'em!