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
Another one Sushila — let's solve it. Step 1: Rewrite the expression using the given hint. The expression is 2^224 ÷ 4^32. Given the hint 4 = 2^2, we substitute this into the expression: 2^224 ÷ (2^2)^32 Step 2: Simplify the exponent of the second term. Using the exponent rule (a^m)^n = a^mn: (2^2)^32 = 2^2 × 32 = 2^64 The expression becomes: 2^224 ÷ 2^64 Step 3: Simplify the entire expression using exponent rules. Using the exponent rule a^m ÷ a^n = a^m-n: 2^224 - 64 = 2^160 Step 4: Determine the units digit of 2^160. We observe the pattern of the units digits of powers of 2: • 2^1 = 2 • 2^2 = 4 • 2^3 = 8 • 2^4 = 16 6 • 2^5 = 32 2 The pattern of units digits (2, 4, 8, 6) repeats every 4 powers. To find the units digit of 2^160, we divide the exponent (160) by 4 and look at the remainder. 160 ÷ 4 = 40 with a remainder of 0 When the remainder is 0, the units digit is the same as the units digit of 2^4, which is 6. The units digit in the value of 2^224 ÷ 4^32 is 6. Send me the next one 📸