![Evaluate: [8]638 and Simplify: 3/(64)](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1779180377640-bcaf6cd26d6ee8d9.png&w=3840&q=75)
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
wild, let's knock this out. Here are the solutions for problems 4 and 5: 4. Evaluate: [8]63^8 Step 1: Convert the radical expression to exponential form using the rule [n]a^m = a^(m)/(n). [8]63^8 = 63^(8)/(8) Step 2: Simplify the exponent. 63^(8)/(8) = 63^1 Step 3: Evaluate the expression. 63^1 = 63 The evaluated expression is: 63 5. Simplify: 3/(64) Step 1: Apply the property n/(b) = [n]a[n]b to separate the numerator and denominator. 3/(64) = [3]297[3]64 Step 2: Evaluate the cube root of the denominator. [3]64 = [3]4^3 = 4 Step 3: Find the prime factorization of the numerator, 297. 297 = 3 × 99 = 3 × 3 × 33 = 3 × 3 × 3 × 11 = 3^3 × 11 Step 4: Substitute the prime factorization into the numerator's cube root and simplify. [3]297 = [3]3^3 × 11 = [3]3^3 × [3]11 = 3[3]11 Step 5: Combine the simplified numerator and denominator. 3[3]114 The simplified expression is: 3[3]114 Got more? Send 'em 📸