# Express each of the following as the product of powers of their prime factors:

(i) 648 (ii) 405 (iii) 540 (iv) 3,600

**Solution:**

Let's find prime factors of the given number and then raise the prime factor to its powers.

(i) 648

Prime factorization of 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3

In this, 3 is the exponent of 2, and 4 is the exponent of 3

So, 648 can be expressed as the product of powers of their prime factors as 2^{3 }× 3^{4}

(ii) 405

Prime factorization of 405 = 3 × 3 × 3 × 3 × 5

In this, 4 is the exponent of 3, and 1 is the exponent of 5

So, the product of powers of prime factors = 3^{4}^{ }× 5

(iii) 540

Prime factorization of 540 = 2 × 2 × 3 × 3. × 3 × 5

In this, 2 is the exponent of 2. 3 is the exponent of 3, and 1 is the exponent of 5

So, the product of powers of prime factors = 2^{2 }× 3^{3 }× 5

(iv) 3600

Prime factorization of 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

In this, 4 is the exponent of 2. 2 is the exponent of 3, and 2 is the exponent of 5

So, the product of powers of prime factors = 2^{4 }× 3^{2 }× 5^{2}

**Video Solution:**

## Express each of the following as the product of powers of their prime factors: (i) 648 (ii) 405 (iii) 540 (iv) 3,600

### Maths NCERT Solutions Class 7 - Chapter 13 Exercise 13.1 Question 5

**Summary:**

The following can be expressed as the product of powers of their prime factors:(i) 648 can be expressed as the product of powers of their prime factors = 2^{3 }× 3^{4}, (ii) the product of powers of prime factors of 405 = 3^{4}^{ }× 5, (iii) the product of powers of prime factors of 540 = 2^{2 }× 3^{3 }× 5, (iv) the product of powers of prime factors 3,600 = 2^{4 }× 3^{2 }× 5^{2}