(6/13)¹⁰ ÷ [(6/13)⁵]² = (6/13)⁻⁻⁻⁻. Fill in the blanks to make the statement true

Solution:

Given, (6/13)¹⁰ ÷ [(6/13)⁵]² = (6/13)⁻⁻⁻⁻.

We have to fill in the blanks to make the statement true.

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

(a^m)ⁿ = a^mn

Considering [(6/13)⁵]²,

(a^m)ⁿ = [(6/13)⁵]²

Here, a = 6/13

Also, m = 5 and n = 3

Now, mn = 5(2) = 10

a^mn = (6/13)¹⁰

Now, [(6/13)⁵]² = (6/13)¹⁰

The expression becomes (6/13)¹⁰ ÷ (6/13)¹⁰

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

a^m ÷ aⁿ = a^m-n , m>n

= (6/13)¹⁰⁻¹⁰

= (6/13)⁰

Therefore, the required value is (6/13)⁰

✦ Try This: (3/4)¹² ÷ [(3/4)³]² = (3/4)⁻⁻⁻⁻. Fill in the blanks to make the statement true

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

NCERT Exemplar Class 7 Maths Chapter 11 Problem 28

(6/13)¹⁰ ÷ [(6/13)⁵]² = (6/13)⁻⁻⁻⁻. Fill in the blanks to make the statement true

Summary:

(6/13)¹⁰ ÷ [(6/13)⁵]² = (6/13)⁰

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