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 × aⁿ = a^{m + n}

a^m ÷ aⁿ = a^{m - n}

(a^m)ⁿ = a^mn

a⁰ = 1

(i) 108 × 192

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

= 2⁸ × 3⁴ [a^m × aⁿ = a^{m + n}]

(ii) 270

= 2 × 3 × 3 × 3 × 5

= 2 × 3³ × 5 [a^m × aⁿ = a^{m + n}]

= 10 × 3³

(iii) 729 × 64

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

= 3⁶ × 2⁶ [a^m × aⁿ = a^m+n]

= (3 × 2)⁶ [(a^m)ⁿ = a^mn]

= 6⁶

(iv) 768

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

= 2⁸ × 3 [a^m × aⁿ = a^{m + n}]

☛ Check: NCERT Solutions for Class 7 Maths Chapter 13

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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) 2⁸ × 3⁴, (ii) 10 × 3³, (iii) 6⁶, (iv) 2⁸ × 3

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