Question

Evaluate: \((112 \times 5^4)= ?\)

• A. 67000
• B. 70000
• C. 76500
• D. 77200

Hint:

Whenever you see \(n \times 5^k\), use \(5^k=\dfrac{10^k{2^k\). Divide \(n\) by \(2^k\) first (if possible) and then just append zeros by multiplying with \(10^k\).

Answer 1

The Correct Option is B

Step 1 (Power first).
\(5^4 = 5\times5\times5\times5 = 25 \times 25 = 625.\)
Step 2 (Direct multiplication).
\(112 \times 625 = (100 \times 625) + (12 \times 625) = 62500 + 7500 = 70000.\)
Step 3 (Check with a fraction trick).
Use \(5^4 = \dfrac{10^4}{2^4} = \dfrac{10000}{16}\). Then \[ 112 \times 5^4 \;=\; 112 \times \frac{10000}{16} \;=\; \frac{112}{16}\times 10000 \;=\; 7 \times 10000 \;=\; 70000. \] Both methods agree. \[ \boxed{70000 \ \text{(Option (b)}} \]