ch- Exponents and powers Concept product of prime factors - Exponential form Write expanded form of 'P? "
Answers
Step-by-step explanation:
Any positive integer can be written as a unique product of prime numbers.
For example, to break 540 down to its prime factors, I simply start dividing by prime numbers:
540 is even, so 2 goes into it: 540 / 2 = 270.
270 is even, so 2 goes into it: 270 / 2 = 135.
3 goes into 135 (because 1+3+5=9 and 3 goes into 9), so 135 / 3 = 45.
5 goes into 45, so 45 / 5 = 9.
3 goes into 9, so 9 / 3 = 3.
3 goes into itself, so 3 / 3 = 1. When I get to 1, I stop.
Now I list what I divided by: 2, 2, 3, 5, 3, 3. When I multiply all these together I will get the original number:
2 × 2 × 3 × 5 × 3 × 3 = 540.
To write this in exponential form, I just re-order it to group the prime numbers together:
2 × 2 × 3 × 3 × 3 × 5
And then count the number of times each factor appears:
22 × 33 × 51.
Usually, when an exponent is 1, we don't write it because it is assumed, so our final answer is:
22 × 33 × 5.
Now you try it by breaking down 48 into its prime factors