(-3/5)¹⁰⁰ = (-3)¹⁰⁰/(-5)¹⁰⁰. State whether the given statement is true or false

Solution:

Given, (-3/5)¹⁰⁰ = (-3)¹⁰⁰/(-5)¹⁰⁰.

We have to determine if the given statement is true or false.

Considering (-3/5)¹⁰⁰,

(-3/5)¹⁰⁰ = [(-1 × 3)/5]¹⁰⁰

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

(a×b)^m = a^m × b^m

= (-1)¹⁰⁰ × (3)¹⁰⁰ / (5)¹⁰⁰

We know, (-1)ⁿ = 1, if n = even number

Here, n = 100, n is even number

So, (-1)¹⁰⁰ = 1

(-3/5)¹⁰⁰ = (3)¹⁰⁰/(5)¹⁰⁰ —-------------------- (1)

Considering (-3)¹⁰⁰/(-5)¹⁰⁰,

Cancelling out common negative sign,

(-3)¹⁰⁰/(-5)¹⁰⁰ = (3)¹⁰⁰/(5)¹⁰⁰ —-------------- (2)

From (1) and (2),

(-3/5)¹⁰⁰ = (-3)¹⁰⁰/(-5)¹⁰⁰ which means that the given statement is true.

✦ Try This: (-2/3)¹⁰ = (-2)¹⁰/(-5)¹⁰. State whether the given statement is true or false

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

NCERT Exemplar Class 7 Maths Chapter 11 Problem 46

(-3/5)¹⁰⁰ = (-3)¹⁰⁰/(-5)¹⁰⁰. State whether the given statement is true or false

Summary:

The given statement,”(-3/5)¹⁰⁰ = (-3)¹⁰⁰/(-5)¹⁰⁰” is true

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