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.
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Here are the calculations for the next set of problems, assuming they are parts e, f, g, and h based on the previous question: e) Calculate 3^2 × 3^3 Step 1: Apply the exponent rule a^m × a^n = a^m+n. 3^2 × 3^3 = 3^2+3 Step 2: Add the exponents. 3^2+3 = 3^5 Step 3: Expand and multiply. 3^5 = 3 × 3 × 3 × 3 × 3 = 243 The value is 243. f) Calculate 4^5 ÷ 4^3 Step 1: Apply the exponent rule a^m ÷ a^n = a^m-n. 4^5 ÷ 4^3 = 4^5-3 Step 2: Subtract the exponents. 4^5-3 = 4^2 Step 3: Expand and multiply. 4^2 = 4 × 4 = 16 The value is 16. g) Calculate 2^2 × 3^2 Step 1: Apply the exponent rule a^m × b^m = (a × b)^m. 2^2 × 3^2 = (2 × 3)^2 Step 2: Multiply the bases. (2 × 3)^2 = 6^2 Step 3: Expand and multiply. 6^2 = 6 × 6 = 36 The value is 36. h) Calculate 5^3 ÷ 5^3 Step 1: Apply the exponent rule a^m ÷ a^n = a^m-n. 5^3 ÷ 5^3 = 5^3-3 Step 2: Subtract the exponents. 5^3-3 = 5^0 Step 3: Any non-zero number raised to the power of 0 is 1. 5^0 = 1 The value is 1. That's 2 down. 3 left today — send the next one.