Say true or false and justify your answer: (i) 10 × 10¹¹ = 100¹¹ (ii) 2³ > 5² (iii) 2³ × 3² = 6⁵ (iv) 3⁰ = 1000⁰

Solution:

To solve this question, we will be using the laws of exponents.

(i) 10 × 10¹¹ = 100¹¹

LHS = 10 × 10¹¹ = 10^{11 + 1} = 10¹² [a^m × aⁿ = a^{m + n}]

RHS = 100¹¹ = (10² )¹¹ = 10²² [(a^m)ⁿ = a^mn]

Therefore,10¹² ≠ 10²²

Thus, the statement is false.

(ii) 2³ > 5²

LHS = 2³ = 2 × 2 × 2 = 8

RHS = 5² = 5× 5 = 25

Therefore, 2³ < 5²

Thus, the statement is false.

(iii) 2³ × 3² = 6⁵

LHS = 2³ × 3² = 2 × 2 × 2 × 3 × 3 = 72

RHS = 6⁵ = 6 × 6 × 6 × 6 × 6 = 7776

Therefore, 2³ × 3² ≠ 6⁵

Thus, the statement is false.

(iv) 3⁰ = 1000⁰ = 1 [Since, a⁰ = 1]

Thus, the statement is true.

☛ Check: NCERT Solutions for Class 7 Maths Chapter 13

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Video Solution:

Say true or false and justify your answer: (i) 10 × 10¹¹ = 100¹¹ (ii) 2³ > 5² (iii) 2³ × 3² = 6⁵ (iv) 3⁰ = 1000⁰

Maths NCERT Solutions Class 7 Chapter 13 Exercise 13.2 Question 3

Summary:

For the following (i) 10 × 10¹¹ = 100¹¹ (ii) 2³ > 5² (iii) 2³ × 3² = 6⁵ (iv) 3⁰ = 1000⁰ are as follows: (i) False, (ii) False, (iii) False, (iv) True

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