The age of the universe is around 100,000,000,000,000,000s. a top quark has a lifetime of roughly 0.1s. writing numbers out with all these zeros is not very convenient. such quantities are usually written as powers of 10. the age of the universe can be written as 1017s and the lifetime of a top quark as 10−24s.

how many top quark lifetimes have there been in the history of the universe (i. e., what is the age of the universe divided by the lifetime of a top quark)? note that these powers of 10 follow the same rules that any exponents would follow.

10⁴¹ s quark top lives have been in the history of the universe.

Explanation:

You need to determine how many quark top lives there have been in the history of the universe, that is, what is the age of the universe divided by the lifetime of a top quark. Expressed in a formula, this is:

Yo know that the "Age of the universe" is 100,000,000,000,000,000  which can also be expressed as 10¹⁷ s .

You also know that the "Lifetime of a top quark" is 0.000000000000000000000001 which can also be expressed as 10⁻²⁴ s.

Then

Recalling that the result of dividing two powers of the same base is another power with the same base where the exponent is the subtraction of the initial exponents, it is possible to calculate this division as follows:

t=10⁴¹ s

So 10⁴¹ s quark top lives have been in the history of the universe.