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Simplify and express the following in exponential form: (3⁷ ÷ 3⁵)⁴

Solution:

Given, the expression is (3⁷ ÷ 3⁵)⁴

We have to write the expression in exponential form.

Considering 3⁷ ÷ 3⁵,

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

a^m ÷ aⁿ = a^{m - n}

Here, a = 3, m = 7 and n = 5

m - n = 7 - 5 = 2

a^{m - n} = (3)²

So, 3⁷ ÷ 3⁵ = 3²

Now, (3⁷ ÷ 3⁵)⁴ = (3²)⁴

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

(a^m)ⁿ = (a)^mn

Considering (3²)⁴,

Here, a = 3, m = 2 and n = 4

= (3)^{2 × 4}

= 3⁸

Therefore, the exponential form is 3⁸.

✦ Try This: Simplify and express the following in exponential form: (a⁷ ÷ a⁵)⁷

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

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

Summary:

The exponential form of the expression (3⁷ ÷ 3⁵)⁴ is 3⁸

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