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: Simplify (a^3)^2. Using the rule (a^m)^n = a^m × n: (a^3)^2 = a^3 × 2 = a^6 The simplified expression is a^6. Step 2: Simplify (b^2)^4. Using the rule (a^m)^n = a^m × n: (b^2)^4 = b^2 × 4 = b^8 The simplified expression is b^8. Step 3: Simplify (c^5)^3. Using the rule (a^m)^n = a^m × n: (c^5)^3 = c^5 × 3 = c^15 The simplified expression is c^15. Step 4: Simplify (d^4)^3. Using the rule (a^m)^n = a^m × n: (d^4)^3 = d^4 × 3 = d^12 The simplified expression is d^12. Step 5: Simplify (e^3)^3. Using the rule (a^m)^n = a^m × n: (e^3)^3 = e^3 × 3 = e^9 The simplified expression is e^9. Step 6: Simplify (f^0)^8. First, simplify f^0. Using the rule a^0 = 1: f^0 = 1 Then, substitute this back into the expression: (f^0)^8 = (1)^8 = 1 The simplified expression is 1. Step 7: Simplify (g^-2)^5. Using the rule (a^m)^n = a^m × n: (g^-2)^5 = g^-2 × 5 = g^-10 Using the rule a^-n = (1)/(a^n): g^-10 = (1)/(g^10) The simplified expression is (1)/(g^10). Step 8: Simplify (h^4)^-5. Using the rule (a^m)^n = a^m × n: (h^4)^-5 = h^4 × (-5) = h^-20 Using the rule a^-n = (1)/(a^n): h^-20 = (1)/(h^20) The simplified expression is (1)/(h^20). Step 9: Simplify (5^2)^-1. First, calculate 5^2: 5^2 = 25 Then, substitute this back into the expression: (5^2)^-1 = (25)^-1 Using the rule a^-n = (1)/(a^n): (25)^-1 = (1)/(25^1) = (1)/(25) The simplified expression is (1)/(25). Step 10: Simplify (3^-2)^-2. Using the rule (a^m)^n = a^m × n: (3^-2)^-2 = 3^-2 × (-2) = 3^4 Calculate the value: 3^4 = 3 × 3 × 3 × 3 = 81 The simplified expression is 81. Step 11: Simplify (10^2)^7. Using the rule (a^m)^n = a^m × n: (10^2)^7 = 10^2 × 7 = 10^14 The simplified expression is 10^14. Step 12: Simplify (2^-3)^2. Using the rule (a^m)^n = a^m × n: (2^-3)^2 = 2^-3 × 2 = 2^-6 Using the rule a^-n = (1)/(a^n): 2^-6 = (1)/(2^6) Calculate the value: (1)/(2^6) = (1)/(2 × 2 × 2 × 2 × 2 × 2) = (1)/(64) The simplified expression is (1)/(64). 3 done, 2 left today. You're making progress.