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: Rewrite all bases as powers of 2. We know that 16 = 2^4 and 8 = 2^3. The expression becomes: 2^m^2 × (2^4)^m^2(2^3)^m-n × 2^m+n Step 2: Apply the exponent rule (a^b)^c = a^bc. 2^m^2 × 2^4 × m^22^3 × (m-n) × 2^m+n 2^m^2 × 2^4m^22^3m-3n × 2^m+n Step 3: Apply the exponent rule a^b × a^c = a^b+c to combine terms in the numerator and denominator. Numerator: 2^m^2 × 2^4m^2 = 2^m^2 + 4m^2 = 2^5m^2 Denominator: 2^3m-3n × 2^m+n = 2^(3m-3n) + (m+n) = 2^3m-3n+m+n = 2^4m-2n Now the expression is: 2^5m^22^4m-2n Step 4: Apply the exponent rule (a^b)/(a^c) = a^b-c. 2^5m^2 - (4m-2n) Step 5: Simplify the exponent. 2^5m^2 - 4m + 2n The simplified expression is: 2^5m^2 - 4m + 2n