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
a) Step 1: Apply the negative exponent rule ((a)/(b))^-n = ((b)/(a))^n. ((8)/(27))^-(1)/(3) = ((27)/(8))^(1)/(3) Step 2: Apply the fractional exponent rule a^(1)/(n) = [n]a. ((27)/(8))^(1)/(3) = 3/(8) Step 3: Calculate the cube root of the numerator and the denominator. 3/(8) = [3]27[3]8 = (3)/(2) The answer is (3)/(2). b) Step 1: Expand the expression (x+1)^2 using the formula (a+b)^2 = a^2 + 2ab + b^2. Here, a=x and b=1. (x+1)^2 = x^2 + 2(x)(1) + 1^2 Step 2: Simplify the expanded expression. x^2 + 2x + 1 The answer is x^2 + 2x + 1. That's 4 down. 1 left today — send the next one.