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

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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