Respuesta :
Answer:
I got 5^10 x 2^14 x 3
Step-by-step explanation:
1. Do a tree to find 480 as a product of its prime factors
2. You should get 480= 5x2x3x2x2x2x2
3. 10 expressed as a product of its prime factors is 5x2
4. so 10^9 expressed as a product of its prime factors would be
5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2
5. You can then write out 480x10^9 as a product of its prime factors
5x2x3x2x2x2x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2
6. change this to use powers
5^10 x 2^14 x 3
N = 5^(10) × 2^(14) × 3
This is about prime factors
By definition, a prime factor is a factor of a number and that factor is also a prime number.
A prime number is one that is divisible by only itself and 1.
The number we have is; 480 × 10^(9)
Now, let's list the prime factors or 480 and they are;
2, 3, 5
Now, using these prime factors alone to get 480, we have;
5 × 3 × 2 × 2 × 2 × 2 × 2 = 480
In powers, gives;
5 × 3 × 2^(5)
Now,the 10^(9) with the 480 can also be expressed in terms of it's prime factors which are 2 and 5 as;
(5 × 2)^(9)
Expanding this gives; 5^(9) × 2^(9) = 10^(9)
Thus;
480 × 10^(9) = 5 × 3 × 2^(5) × 5^(9) × 2^(9)
This gives;
5^(10) × 2^(14) × 3
Read more at; brainly.com/question/4853862
