Simplify the exponential expression: (2^5 * 8^2) / 4^4.
Answer and explanation
Correct answer: C. 8
- Step 1: Convert all terms to base 2: 8 = 2^3 => 8^2 = (2^3)^2 = 2^6; 4 = 2^2 => 4^4 = (2^2)^4 = 2^8.
- Step 2: Rewrite numerator: 2^5 * 2^6 = 2^(5+6) = 2^11.
- Step 3: Divide by denominator: 2^11 / 2^8 = 2^(11-8) = 2^3 = 8.
Answer
8.
Why not the others: Option 16 results from evaluating 2^4. Option 4 underestimates powers in 8^2. Option 32 evaluates 2^5 without subtracting the full exponent 8.
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