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
Here are the solutions to the problems: a) Determine the value of 6^0 + 6^0 Step 1: Apply the rule that any non-zero number raised to the power of 0 is 1. 6^0 = 1 Step 2: Substitute the value and perform the addition. 6^0 + 6^0 = 1 + 1 = 2 The value is 2. b) Determine the value of 4^1 × 2^2 × 3^1 Step 1: Evaluate each term. 4^1 = 4 2^2 = 2 × 2 = 4 3^1 = 3 Step 2: Multiply the evaluated terms. 4 × 4 × 3 = 16 × 3 = 48 The value is 48. c) Determine the value of (8^4)/(2) Step 1: Express the base 8 as a power of 2. 8 = 2^3 Step 2: Substitute 2^3 for 8 in the expression. ((2^3)^4)/(2) Step 3: Apply the exponent rule (a^m)^n = a^m × n. 2^3 × 42 = 2^122^1 Step 4: Apply the exponent rule (a^m)/(a^n) = a^m-n. 2^12-1 = 2^11 Step 5: Calculate the value of 2^11. 2^11 = 2048 The value is 2048. d) Determine the value of (81 × 243)/(27^2 × 3^6) Step 1: Express all numbers as powers of 3. 81 = 3 × 3 × 3 × 3 = 3^4 243 = 3 × 3 × 3 × 3 × 3 = 3^5 27 = 3 × 3 × 3 = 3^3 Step 2: Substitute these into the expression. (3^4 × 3^5)/((3^3)^2 × 3^6) Step 3: Apply the exponent rule (a^m)^n = a^m × n to the denominator. (3^3)^2 = 3^3 × 2 = 3^6 Step 4: Rewrite the expression with all terms as powers of 3. (3^4 × 3^5)/(3^6 × 3^6) Step 5: Apply the exponent rule a^m × a^n = a^m+n to the numerator and denominator. Numerator: 3^4 × 3^5 = 3^4+5 = 3^9 Denominator: 3^6 × 3^6 = 3^6+6 = 3^12 Step 6: Rewrite the expression. (3^9)/(3^12) Step 7: Apply the exponent rule (a^m)/(a^n) = a^m-n. 3^9-12 = 3^-3 Step 8: Apply the exponent rule a^-n = (1)/(a^n). 3^-3 = (1)/(3^3) Step 9: Calculate the final value. (1)/(3 × 3 × 3) = (1)/(27) The value is (1)/(27). That's 2 down. 3 left today — send the next one.