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Simplify and express the following in exponential form: (5¹⁵ ÷ 5¹⁰) × 5⁵

Solution:

Given, the expression is (5¹⁵ ÷ 5¹⁰) × 5⁵

We have to write the expression in exponential form.

Considering 5¹⁵ ÷ 5¹⁰,

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

a^m ÷ aⁿ = a^{m - n}

Here, a = 5, m = 15 and n = 10

m - n = 15 - 10 = 5

a^{m - n} = (5)⁵

So, 5¹⁵ ÷ 5¹⁰ = 5⁵

Now, (5¹⁵÷ 5¹⁰) × 5⁵ = 5⁵ × 5⁵

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

a^m × aⁿ = a^{m + n}

Considering 5⁵ × 5⁵,

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

m + n = 5 + 5 = 10

5⁵ × 5⁵ = 5¹⁰

So, (5¹⁵ ÷ 5¹⁰) × 5⁵ = 5¹⁰

Therefore, the exponential form is 5¹⁰.

✦ Try This: Simplify and express the following in exponential form: (6¹⁵ ÷ 6¹⁰) × 4⁵

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

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

Summary:

The exponential form of the expression (5¹⁵ ÷ 5¹⁰) × 5⁵ is 5¹⁰.

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