if a^1*b^2*c^3=6000,where a,b and c are natural numbers,then what is the value of a*b*c?

Given, a¹× b²×c³=6000

It can be solved by prime factorizing the 6000 as:

6000 = 2 × 3000

= 2 × 2 × 1500 =  2 × 2 × 2 × 750

=  2 × 2 × 2 × 2 × 375

=  2 × 2 × 2 × 2 × 3 × 125

=  2 × 2 × 2 × 2 × 3 × 5 × 5 × 5

= 3¹  × 4² × 5³ 

On comparing 3¹  × 4² × 5³ with a¹  × b² × c³, we get

a = 3, b = 4 and c = 5

Now, a × b × c = 3×4×5 = 60