Using laws of exponents, simplify and write the answer in exponential form:
(i) 3² × 3⁴ × 3⁸    (ii) 6¹⁵ ÷ 6¹⁰   (iii) a³ × a²    (iv) 7^x × 7²
(v) (5²)³ ÷ 5³    (vi) 2⁵ × 5⁵    (vii) a⁴ × b⁴    (viii) (3⁴ )³
(ix) (2²⁰ ÷ 2¹⁵) × 2³    (x) 8^t ÷ 8²

Solution:

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

Here are some important laws of exponents

1.) a^m × aⁿ = a^{m + n}

2.) a^m × b^m = (ab)^m

3.) a^m ÷ aⁿ = a^{m - n}

4.) (a^m)ⁿ = a^mn

5.) a^o = 1

(i) 3² × 3⁴ × 3⁸ = 3^{2 + 4 + 8} = 3¹⁴ [a^m × aⁿ = a^{m + n}]

(ii) 6¹⁵ ÷ 6¹⁰ = 6^{15 - 10} = 6⁵ [a^m ÷ aⁿ = a^{m - n}]

(iii) a³ × a² = a^3 + 2 = a⁵ [a^m × aⁿ = a^{m + n}]

(iv) 7^x × 7² = 7^{x + 2} [a^m × aⁿ = a^{m + n}]

(v) (5² )³ ÷ 5³ = 5⁶ ÷ 5³ [(a^m)ⁿ = a^mn]

= 5^{6 - 3} [a^m ÷ aⁿ = a^{m - n}]

= 5³

(vi) 2⁵ × 5⁵ = (2 × 5)⁵ [a^m × b^m = (ab)^m]

= 10⁵

(vii) a⁴ × b⁴ = (ab)⁴ [a^m × b^m = (ab)^m]

(viii) (3⁴ )³ = 3¹² [(a^m)ⁿ = a^{m n}]

(ix) (2²⁰ ÷ 2¹⁵ )× 2³ = 2^{20 - 15} × 2³ [a^m ÷ aⁿ = a^{m - n}]

= 2⁵ × 2³

= 2⁸ [a^m × aⁿ = a^{m + n}]

(x) 8^t ÷ 8² = 8^t - 2 [a^m ÷ aⁿ = a^{m - n}]

☛ Check: NCERT Solutions for Class 7 Maths Chapter 13

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Video Solution:

Using laws of exponents, simplify and write the answer in exponential form: (i) 3² × 3⁴ × 3⁸ (ii) 6¹⁵ ÷ 6¹⁰ (iii) a³ × a² (iv) 7ˣ × 7² (v) (5² )³ ÷ 5³ (vi) 2⁵ × 5⁵ (vii) a⁴ × b⁴ (viii) (3⁴ )³ (ix) (2²⁰ ÷ 2¹⁵ ) × 2³ (x) 8ᵗ ÷ 8²

Maths NCERT Solutions Class 7 Chapter 13 Exercise 13.2 Question 1

Summary:

Using laws of exponents, we have simplified and have written the answer in exponential form: (i) 3² × 3⁴ × 3⁸ (ii) 6¹⁵ ÷ 6¹⁰ (iii) a³ × a² (iv) 7^x × 7² (v) (5² )³ ÷ 5³ (vi) 2⁵ × 5⁵ (vii) a⁴ × b⁴ (viii) (3⁴ )³ (ix) (2²⁰ ÷ 2¹⁵ ) × 2³ (x) 8^t ÷ 8² as follows (i) 3¹⁴, (ii) 6⁵ , (iii) a⁵ , (iv) 7^{x + 2}, (v) 5³, (vi)10⁵, (vii) (ab)⁴, (viii) 3¹², (ix) 2⁸, (x) 8^{t - 2}

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