Question

What is the highest power of 2 in the expression(1800*25*4^8*21^2*45^(-2))?
a)20
b)21
c)19
d)18
e)17

Answer 1

Answer:

21 is the highest power

Answer 2

c)19

Given:

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.