[(-1/4)¹⁶]² = (-1/4)⁻⁻⁻. Fill in the blanks to make the statement true.

Solution:

Given, [(-1/4)¹⁶]² = (-1/4)⁻⁻⁻.

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 [(-1/4)¹⁶]²,

(a^m)ⁿ = [(-1/4)¹⁶]²

Here, a = -1/4

Also, m = 16 and n = 2

Now, mn = 16(2) = 32

a^mn = (-1/4)³²

Therefore, the required value is (-1/4)³².

✦ Try This: [(-2/3)⁷]² = (-2/3)⁻⁻⁻. 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 29

[(-1/4)¹⁶]² = (-1/4)⁻⁻⁻. Fill in the blanks to make the statement true

Summary:

[(-1/4)¹⁶]² = (-1/4)³²

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