Express 10500 in terms of its prime factors . determine the smallest positive number P such that 10500P is a perfect cube

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Step-by-step explanation:

Dividing by prime numbers :

2 | 10500

2 |   5250

3 |    2625  

5 |       875

5 |        175

5 |          35

                7.

So 10500 = 2*2*3*5*5*5*7

To find the smallest positive cube  we need to multiply by 2 ( to get 3 2's in the prime factors), another 2 3's and another 2 7's

That is P = 2*3*3*7*7 =  882.

The perfect cube is 2^3*3^3*5*3*7^3 = 9261000.