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Simplify and express the following in exponential form: [(3/7)⁴×(3/7)⁵]÷(3/7)⁷

Solution:

Given, the expression is [(3/7)⁴ × (3/7)⁵] ÷ (3/7)⁷

We have to write the expression in exponential form.

Considering [(3/7)⁴ × (3/7)⁵],

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

a^m × aⁿ = a^{m + n}

Here, a = 3/7, m = 4 and n = 5

m + n = 4 + 5 = 9

a^{m + n} = (3/7)⁹

So, [(3/7)⁴ × (3/7)⁵] = (3/7)⁹

Now, [(3/7)⁴ × (3/7)⁵] ÷ (3/7)⁷ = (3/7)⁹ ÷ (3/7)⁷

Considering (3/7)⁹ ÷ (3/7)⁷,

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

a^m ÷ aⁿ = a^{m - n}

Here, a = 3/7, m = 9 and n = 7

m - n = 9 - 7 = 2

a^{m - n} = (3/7)²

So, (3/7)⁹ ÷ (3/7)⁷ = (3/7)²

Therefore, [(3/7)⁴ × (3/7)⁵] ÷ (3/7)⁷ = (3/7)²

✦ Try This: Simplify and express the following in exponential form: [(-1/4)⁴ × (-1/4)⁵] ÷ (-1/4)⁷

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

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

Summary:

The exponential form of the expression [(3/7)⁴×(3/7)⁵]÷(3/7)⁷ is (3/7)²

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