Maths Class 7 Exponents & Powers Chapter 11 Exercise 11.2 Question Answer

Solutions For All Chapters Maths Class 7

Ex 11.2 Class 7 Maths Question 1.
Using laws of e×ponents, simplify and write the answer in e×ponential 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:

(i) 3² × 3⁴ × 3⁸ = 3²+4+8 = 3¹⁴ [am ÷ an = am+n]

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

(iii) a³ × a² = a³+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 = 5^2×3 ÷ 5³ = 5⁶ ÷ 5³ = 5^6-3 = 5³ [(a³)ⁿ = a^mn, a^m ÷ aⁿ = a^m-n]

(vi) 2⁵ × 5⁵ = (2 × 5)⁵ = 10⁵ [a^m × b^m = (ab)^m]

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

(ix) (2²⁰ ÷ 2¹⁵) × 2³ = 2^20-15 × 2³

=2⁵ × 2³ = 2⁵⁺³ = 2⁸

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

Ex 11.2 Class 7 Maths Question 2.
Simplify and express each of the following in exponential form:

Solution:

Ex 11.2 Class 7 Maths Question 3.
Say true or false and justify your answer:

(i) 10 × 10¹¹ = 100¹¹

(ii) 2³ > 5² 

(iii) 2³ × 3² = 6⁵

(iv) 3²⁰ = (1000)⁰

Solution:

(i) 10 × 10¹¹ = 10¹⁺¹¹ = 10¹²

RHS = 100¹¹ = (10²)¹¹ = 10²²

10¹² ≠ 10²²

∴ Statement is false.

(ii) 2³ > 5²

LHS = 2³ = 8

RHS = 5²2 = 25

8 < 25

∴ 2³ < 5²
Thus, the statement is false.

(iii) 2³ × 3² = 6⁵

LHS = 2³3 × 3² = 8 × 9 = 7²

RHS = 6⁵ = 6 × 6 × 6 × 6 × 6 = 7776

∴ 72 ≠ 7776

∴ The statement is false.

(iv) (iv) 3⁰ = (1000)⁰

⇒ 1 = 1 True [∵ a⁰ = 1]

Ex 11.2 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

=2⁸ × 3⁴

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

=3⁶ × 2⁶

Ex 11.2 Class 7 Maths Question 5.
Simplify:

Solution: