What is the highest power of 2 in the following expression? 1800 × 25 × 4^8 × 21^2 × 45^(−2)

Aptitude and Reasoning MCQ Questions with Solutions

What is the highest power of 2 in the following expression? 1800 × 25 × 4⁸ × 21² × 45^(-2)

A) 19
B) 21
C) 20
D) 18

Answer & Explanation:

A) 19
1800 x 25 x 4⁸ x 21² x 45 ⁽⁻²⁾
Now we will simplify them in the terms of 2, 3, and 5
= 2³ x 3² x 5² x 5² x (2²)⁸ x (3 x 7)² x (3² x 5)⁽⁻²⁾
= 2³ x 3² x 5² x 5² x 2¹⁶ x 3² x 7² x 3⁻⁴ x 5⁻²
∵ aᵇ x aⁿ = aᵇ⁺ⁿ
= 2 ³⁺¹⁶ x 3²⁺²⁻⁴ x 5²⁺²⁻²
= 2¹⁹ x 3⁰ x 5²
Hence, the highest power of 2 in the expression 1800 x 25 x 4⁸ x 21² x 45 ⁽⁻²⁾ is 19.

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