If 5.12 × 50625 × 0.5488 = $2^a3^b5^c7^d$, then find the value of a + b + c + d.
12
Correct Answer: 12
Prime factorisations:
- 5.12 = 512/100 = 2⁹/(2²×5²) = 27/5²
- 50625 = 225² = (3²×5²)² = 34×54
- 0.5488 = 5488/10000 = (24×73)/(24×54) = 73/54
Product = 27/5² × 34×54 × 73/54
= 27 × 34 × 5(4−2−4) × 73
= 27 × 34 × 5−2 × 73
So a=7, b=4, c=−2, d=3
a+b+c+d = 7+4+(−2)+3 = 12
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