Question

The number of factors in the expression 6² x 2⁴ x 30​

Answer 1

Answer:

Number of factors is 50

Simply firstly write the equation in simplest form

6×6×6×6×5 = 2⁴×3⁴×5¹

let any factor of the number be (2^x) (3^y) (5^z)

Number of ways of selecting x , y , z is

For x : 4+1

For y : 4+1

For z : 1+1

So number of ways of selecting x , y , “and” z is

(4+1)((4+1)(1+1) = 5×5×2 = 50