Answer :
Final answer:
The given numbers can be factored into prime factors as follows: a. 54 = 2 × 3 × 3 × 3, b. 84 = 2 × 2 × 3 × 7, c. 96 = 2 × 2 × 2 × 2 × 2 × 3, d. 154 = 2 × 7 × 11, e. 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, f. 495 = 3 × 3 × 5 × 11, g. 729 = 3 × 3 × 3 × 3 × 3 × 3, h. 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
Explanation:
a. 54 = 2 × 3 × 3 × 3 = 2 × (3 × 3 × 3) = 2 × 3³
b. 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7
c. 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3
d. 154 = 2 × 7 × 11
e. 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁸
f. 495 = 3 × 3 × 5 × 11
g. 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3⁶
h. 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2¹⁰
Final answer:
To decompose the given numbers into prime factors, we find the prime numbers that multiply together to make the given number. Example decompositions are provided.
Explanation:
To decompose numbers into prime factors, we need to find the prime numbers that multiply together to make the given number. Let's decompose the given numbers:
- 54: 2 x 3 x 3 x 3 = 2^1 x 3^3
- 84: 2 x 2 x 3 x 7 = 2^2 x 3 x 7
- 96: 2 x 2 x 2 x 2 x 2 x 3 = 2^5 x 3
- 154: 2 x 7 x 11 = 2 x 7 x 11
- 256: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^8
- 495: 3 x 3 x 5 x 11 = 3^2 x 5 x 11
- 729: 3 x 3 x 3 x 3 x 3 x 3 = 3^6
- 1024: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^10
Learn more about Decomposing numbers into prime factors here:
https://brainly.com/question/22813348
