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
Welcome back Mc — been a while! Let's pick up where you left off. 1.1.1 Step 1: Observe the values in the table for 2^n: 2, 4, 8, 16, 32. Step 2: Notice that each value is obtained by multiplying the previous value by 2. The pattern is that each successive value of 2^n is double the previous value. 1.1.2 Step 1: The pattern observed is that each term is multiplied by 2 to get the next term. Step 2: The value for 2^5 is 32. To predict 2^6, multiply 2^5 by 2. 2^6 = 32 × 2 = 64 My reasoning is that the pattern shows each power of 2 is twice the previous power of 2. 1.1.2 (Verification) Step 1: Calculate 2^6 by multiplying 2 by itself 6 times. 2^6 = 2 × 2 × 2 × 2 × 2 × 2 Step 2: Perform the multiplication. 2^6 = 4 × 2 × 2 × 2 × 2 = 8 × 2 × 2 × 2 = 16 × 2 × 2 = 32 × 2 = 64 1.2.1 Step 1: Write each power as repeated multiplication. 2^3 = 2 × 2 × 2 2^4 = 2 × 2 × 2 × 2 Step 2: Combine the repeated multiplications and calculate the product. 2^3 × 2^4 = (2 × 2 × 2) × (2 × 2 × 2 × 2) 2^3 × 2^4 = 8 × 16 = 128 1.2.2.1 Step 1: Sipho's answer is 2^7. Calculate 2^7. 2^7 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128 Step 2: Compare Sipho's result with the calculated answer from 1.2.1. Sipho's answer (2^7 = 128) matches the calculated answer (128). Sipho is Correct. 1.2.2.2 Sipho arrived at 7 by adding the exponents of the original terms, 3 and 4, since 3+4=7. 1.2.3 The general law for the given calculations is: a^m × a^n = a^m+n Send me the next one 📸