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# Using laws of exponents, simplify and write the answer in exponential form:

(i) 3^{2} × 3^{4} × 3^{8 } (ii) 6^{15} ÷ 6^{10} (iii) a^{3} × a^{2 } (iv) 7^{x} × 7^{2 }

(v) (5^{2})^{3} ÷ 5^{3 } (vi) 2^{5} × 5^{5 } (vii) a^{4} × b^{4 } (viii) (3^{4} )^{3}

(ix) (2^{20} ÷ 2^{15}) × 2^{3 } (x) 8^{t} ÷ 8^{2}

**Solution:**

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

Here are some important laws of exponents

1.) a^{m} × a^{n} = a^{m + n}

2.) a^{m} × b^{m} = (ab)^{m}

3.) a^{m} ÷ a^{n} = a^{m - n}

4.) (a^{m})^{n} = a^{mn}

5.) a^{o} = 1

(i) 3^{2} × 3^{4} × 3^{8} = 3^{2 + 4 + 8} = 3^{14} [a^{m} × a^{n} = a^{m + n}]

(ii) 6^{15} ÷ 6^{10} = 6^{15 - 10} = 6^{5} [a^{m} ÷ a^{n} = a^{m - n}]

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

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

(v) (5^{2} )^{3} ÷ 5^{3} = 5^{6} ÷ 5^{3} [(a^{m})^{n} = a^{mn}]

= 5^{6 - 3} [a^{m} ÷ a^{n} = a^{m - n}]

= 5^{3}

(vi) 2^{5} × 5^{5} = (2 × 5)^{5} [a^{m} × b^{m} = (ab)^{m}]

= 10^{5}

(vii) a^{4} × b^{4} = (ab)^{4} [a^{m} × b^{m} = (ab)^{m}]

(viii) (3^{4} )^{3} = 3^{1}^{2} [(a^{m})^{n} = a^{m n}]

(ix) (2^{20} ÷ 2^{15} )× 2^{3} = 2^{20 - 15} × 2^{3} [a^{m} ÷ a^{n} = a^{m - n}]

= 2^{5} × 2^{3}

= 2^{8} [a^{m} × a^{n} = a^{m + n}]

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

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

**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) 3^{2} × 3^{4} × 3^{8 }(ii) 6^{15} ÷ 6^{10} (iii) a^{3} × a^{2 }(iv) 7^{x} × 7^{2 }(v) (5^{2} )^{3} ÷ 5^{3 }(vi) 2^{5} × 5^{5 }(vii) a^{4} × b^{4 }(viii) (3^{4} )^{3} (ix) (2^{20} ÷ 2^{15} ) × 2^{3 }(x) 8^{t} ÷ 8^{2} as follows (i) 3^{14}, (ii) 6^{5} , (iii) a^{5} , (iv) 7^{x + 2}, (v) 5^{3}, (vi)10^{5}, (vii) (ab)^{4}, (viii) 3^{12}, (ix) 2^{8}, (x) 8^{t - 2}

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