Which shows 368368 decomposed into a product of powers?

22×4−1×2−222×4-1×2-2

32×2−1×1−232×2-1×1-2

62×2−1×2−2

To decompose the number **368,368** into a product of powers, we'll first perform prime factorization and then express the result in terms of powers of prime numbers.

### Step 1: Prime Factorization of 368,368
We'll start by breaking down 368,368 into its prime factors.

Performing prime factorization:
\[
368368 = 2^5 \times 7 \times 13171
\]
13171 is further factorable:
\[
13171 = 131 \times 101
\]

Thus, the full prime factorization of **368,368** is:
\[
368368 = 2^5 \times 7 \times 131 \times 101
\]

### Step 2: Express as a Product of Powers
Now, we express **368,368** in its final form as a product of powers:
\[
368368 = 2^5 \times 7^1 \times 131^1 \times 101^1
\]

None of the options listed in the question exactly match this factorization.

If you meant to ask about different expressions or breakdowns, feel free to clarify.

Would you like more details or have any questions?

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**Related Questions:**

1. What is the significance of prime factorization in number theory?
2. How can prime numbers be used in cryptography?
3. How would you approach factoring a large number efficiently?
4. Can composite numbers always be factored into primes?
5. What role do exponents play in simplifying large numbers?

**Tip:** When prime factorizing a number, always check if small primes like 2, 3, 5, or 7 divide evenly before moving on to larger primes.

Which shows 368368 decomposed into a product of powers? 22×4−1×2−222×4-1×2-2, 32×2−1×1−232×2-1×1-2, 62×2−1×2−2

Explore the prime factorization of 368368, breaking it down into a product of powers. Learn how to express numbers using prime factors, exponents, and understand the steps involved in this essential concept in number theory. Suitable for high school students and beyond.

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