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
let's simplify this expression using the rules of indices. The problem is (32x^10)^(1)/(5). We need to apply the exponent (1)/(5) to both the numerical coefficient and the variable term inside the parentheses. Step 1: Apply the exponent to each factor inside the parentheses. (32x^10)^(1)/(5) = 32^(1)/(5) · (x^10)^(1)/(5) Step 2: Evaluate 32^(1)/(5). This means finding the fifth root of 32. We know that 2 × 2 × 2 × 2 × 2 = 32. So, 32^(1)/(5) = 2. Step 3: Evaluate (x^10)^(1)/(5) using the power of a power rule (a^m)^n = a^m × n. (x^10)^(1)/(5) = x^10 × (1)/(5) = x^(10)/(5) = x^2 Step 4: Combine the simplified terms. 2 · x^2 = 2x^2 The simplified expression is *2x^2. Drop the next question!