Question

My base is 10. My exponent is an odd number. If you write a multiplication sentence to show my value, it will have fewer than 4 factors of 10. My value is greater than 10. What number am I?

Answer 1

If it is more than 10, then it is not 10^1. The next possibility is 10^3which is 1000, which has factors 2, 5, 10, 20, 25, 40, 50, 80, . . . . . 

What constitutes a "multiplication sentence" exactly ? This is not a standard mathematical term. Do you mean "reduce it to its prime factors" ? 

1000 = 2 x 2 x 2 x 5 x 5 x 5 

which is a lot more than 4 factors. Or not, if you write it as 2³ x 5³. 

But you could say the same about 100 000 = 2^5 x 5^5 

or about 10 000 000 = 2^7 x 5^7 

Take your pick. This is a very badly stated question. 


2. Here we are considering 10^2 or 10^4 . 

10² = 100, with factors 2, 5, 10, 20, 25 - thats more than 3 factors. 

Or, in prime factors, 2 x 2 x 5 x 5 - that's more than 3 factors. 

But exactly the same applies to 10^4 = 10 000 = 2 x 2 x 2 x 5 x 5 x 5 

So again, you take your pick. 

If you want to use invented expressions like "write a multiplication sentence" it is advisable to explain what they mean.