## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.2

- Class 7 Maths Exponents and Powers Exercise 13.1
- Class 7 Maths Exponents and Powers Exercise 13.2
- Class 7 Maths Exponents and Powers Exercise 13.3

**NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.2**

Ex 13.2 Class 7 Maths Question 1.

Using laws of e×ponents, simplify and write the answer in e×ponential 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:

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

(vi) 2^{5} × 5^{5} = (2 × 5)^{5} = 10^{5} [a^{m} × b^{m} = (ab)^{m}]

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

(ix) (2^{20} ÷ 2^{15}) × 2^{3} = 2^{20-15} × 2^{3}

=2^{5} × 2^{3} = 2^{5+3} = 2^{8}

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

Ex 13.2 Class 7 Maths Question 2.

Simplify and express each of the following in exponential form:

Solution:

Ex 13.2 Class 7 Maths Question 3.

Say true or false and justify your answer:

(i) 10 × 10^{11} = 100^{11}

(ii) 2^{3} > 5^{2}

(iii) 2^{3} × 3^{2} = 6^{5}

(iv) 3^{20} = (1000)^{0}

Solution:

(i) 10 × 10^{11} = 10^{1+11} = 10^{12}

RHS = 100^{11} = (10^{2})^{11} = 10^{22}

10^{12} ≠ 10^{22}

∴ Statement is false.

(ii) 2^{3} > 5^{2}

LHS = 2^{3} = 8

RHS = 5^{2}2 = 25

8 < 25

∴ 2^{3} < 5^{2}

Thus, the statement is false.

(iii) 2^{3} × 3^{2} = 6^{5}

LHS = 2^{3}3 × 3^{2} = 8 × 9 = 72

RHS = 6^{5} = 6 × 6 × 6 × 6 × 6 = 7776

∴ 72 ≠ 7776

∴ The statement is false.

(iv) 3^{0} = (1000)^{0}

⇒ 1 = 1 True [∵ a^{0} = 1]

Ex 13.2 Class 7 Maths Question 4.

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:

(i) 108 × 192 = 2 × 2 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

=2^{8} × 3^{4}

(iii) 729 × 64 = 3 × 3 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2

=3^{6} × 2^{6}

Ex 13.2 Class 7 Maths Question 5.

Simplify:

Solution:

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