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
Hey, good to see you again. Step 1: Apply the product rule for exponents, which states that a^m × a^n = a^m+n. In this problem, the base is (-(2)/(3)), and the exponents are -3 and -2. (-(2)/(3))^-3 × (-(2)/(3))^-2 = (-(2)/(3))^-3 + (-2) Step 2: Add the exponents. (-(2)/(3))^-3 - 2 = (-(2)/(3))^-5 Step 3: Apply the rule for negative exponents, which states that a^-n = (1)/(a^n) or ((a)/(b))^-n = ((b)/(a))^n. (-(2)/(3))^-5 = (-(3)/(2))^5 Step 4: Calculate the fifth power of (-(3)/(2)). (-(3)/(2))^5 = ((-3)^5)/((2)^5) (-3)^5 = (-3) × (-3) × (-3) × (-3) × (-3) = -243 (2)^5 = 2 × 2 × 2 × 2 × 2 = 32 Step 5: Substitute the calculated values back into the expression. (-243)/(32) The final answer is -(243)/(32). Send me the next one 📸