# Express each of the following as a product of prime factors only in exponential form: (i) 108 × 192 (ii) 270 (iii) 729 × 64 (iv) 768

**Solution:**

To solve this question, we must remember the laws of exponents.

Here are some important laws of exponents.

a^{m} × a^{n} = a^{m + n}

a^{m} ÷ a^{n} = a^{m - n}

(a^{m})^{n} = a^{m}^{n}

a^{0} = 1

(i) 108 × 192

= 2 × 2 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 3

= 2^{8} × 3^{4} [a^{m} × a^{n} = a^{m + n}]

(ii) 270

= 2 × 3 × 3 × 3 × 5

= 2 × 3^{3} × 5 [a^{m} × a^{n} = a^{m + n}]

= 10 × 3^{3}

(iii) 729 × 64

= 3 × 3 × 3× 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2

= 3^{6} × 2^{6} [a^{m} × a^{n} = a^{m+n}]

= (3 × 2)^{6} [(a^{m})^{n} = a^{m}^{n}]

= 6^{6}

(iv) 768

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

= 2^{8} × 3 [a^{m} × a^{n} = a^{m + n}]

**☛ Check: **NCERT Solutions for Class 7 Maths Chapter 13

**Video Solution:**

## Express each of the following as a product of prime factors only in exponential form: (i) 108 × 192 (ii) 270 (iii) 729 × 64 (iv) 768

Maths NCERT Solutions Class 7 Chapter 13 Exercise 13.2 Question 4

**Summary:**

Each of the following is expressed as a product of prime factors and in exponential form:(i) 2^{8} × 3^{4}, (ii) 10 × 3^{3}, (iii) 6^{6}, (iv) 2^{8} × 3

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