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Simplify and express the following in exponential form: [(3/5)³ × (3/5)⁸] ÷ [(3/5)² × (3/5)⁴]

Solution:

Given, the expression is [(3/5)³ × (3/5)⁸] ÷ [(3/5)² × (3/5)⁴]

We have to write the expression in exponential form.

Considering (3/5)³ × (3/5)⁸,

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

a^m × aⁿ = a^{m + n}

Here, a = 3/5, m = 3 and n = 8

m + n = 3 + 8 = 11

So, (3/5)³ × (3/5)⁸ = (3/5)¹¹

Considering (3/5)² × (3/5)⁴,

Here, a = 3/5, m = 2 and n = 4

m + n = 2 + 4 = 6

So, (3/5)² × (3/5)⁴ = (3/5)⁶

Now, [(3/5)³ × (3/5)⁸] ÷ [(3/5)² × (3/5)⁴] = (3/5)¹¹ ÷ (3/5)⁸

Considering (3/5)¹¹ ÷ (3/5)⁸,

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

a^m ÷ aⁿ = a^{m - n}

Here, a = 3/5, m = 11 and n = 8

m - n = 11 - 8 = 3

So, (3/5)¹¹ ÷ (3/5)⁸ = (3/5)³

Therefore, the exponential form is (3/5)³

✦ Try This: Simplify and express the following in exponential form: [(4/7)³ ÷ (4/7)⁸] ÷ [(4/7)² ÷ (4/7)⁴]

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

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

Summary:

The exponential form of the expression [(3/5)³ × (3/5)⁸] ÷ [(3/5)² × (3/5)⁴] is (3/5)³

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