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: Express all numbers in the expression as powers of 2. We have 4 = 2^2, 8 = 2^3, and 16 = 2^4. Step 2: Substitute these powers into the given expression. (4^3 × 8 × 16^2)/(2^5) = ((2^2)^3 × 2^3 × (2^4)^2)/(2^5) Step 3: Apply the power rule (a^m)^n = a^m × n to simplify the terms in the numerator. 2^2 × 3 × 2^3 × 2^4 × 22^5 = (2^6 × 2^3 × 2^8)/(2^5) Step 4: Apply the product rule a^m × a^n = a^m+n to combine the terms in the numerator. 2^6+3+82^5 = 2^172^5 Step 5: Apply the quotient rule (a^m)/(a^n) = a^m-n to simplify the expression. 2^17-5 = 2^12 The expression in the form 2^n is 2^12. The final answer is 2^12. Send me the next one 📸