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Simplify and express the following in exponential form: [(7/11)⁵ ÷ (7/11)²] × (7/11)²

Solution:

Given, the expression is [(7/11)⁵ ÷ (7/11)²] × (7/11)²

We have to write the expression in exponential form.

Considering [(7/11)⁵ ÷ (7/11)²],

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

a^m ÷ aⁿ = a^{m - n}

Here, a = 7/11, m = 5 and n = 2

m - n = 5 - 2 = 3

a^{m - n} = (7/11)³

So, [(7/11)⁵ ÷ (7/11)²] = (7/11)³

Now, [(7/11)⁵ ÷ (7/11)²] × (7/11)² = (7/11)³ × (7/11)²

Considering (7/11)³ × (7/11)²],

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

a^m × aⁿ = a^{m + n}

Here, a = 7/11, m = 3 and n = 2

m + n = 3 + 2 = 5

a^{m + n} = (7/11)⁵

So, (7/11)³ × (7/11)² = (7/11)⁵

Therefore, [(7/11)⁵ ÷ (7/11)²] × (7/11)² = (7/11)⁵

✦ Try This: Simplify and express the following in exponential form: [(2/3)⁵ ÷ (2/3)²] × (2/3)⁸

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

NCERT Exemplar Class 7 Maths Chapter 11 Problem 84 (b)

Summary:

The exponential form of the expression [(7/11)⁵ ÷ (7/11)²] × (7/11)² is (7/11)⁵

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