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
Step 1: Identify the expression. The expression shown is a power raised to another power: \(-(2)/(3))^-2\^-2 Step 2: Apply the power of a power rule, which states that (a^m)^n = a^m × n. In this case, a = (-(2)/(3)), m = -2, and n = -2. (-(2)/(3))^(-2) × (-2) Step 3: Multiply the exponents. (-(2)/(3))^4 Step 4: Calculate the fourth power of the fraction. When a fraction is raised to a power, both the numerator and the denominator are raised to that power. A negative base raised to an even power results in a positive value. ((-2)^4)/((3)^4) Step 5: Calculate the powers of the numerator and the denominator. (-2)^4 = (-2) × (-2) × (-2) × (-2) = 16 (3)^4 = 3 × 3 × 3 × 3 = 81 Step 6: Combine the results. (16)/(81) The final answer is (16)/(81). 3 done, 2 left today. You're making progress.