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Simplify and express the following in exponential form: (a⁶/a⁴) × a⁵ × a⁰

Solution:

Given, the expression is (a⁶/a⁴) × a⁵ × a⁰

We have to write the expression in exponential form.

Considering a⁶/a⁴,

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

a^m ÷ aⁿ = a^{m - n}

Here, m = 6 and n = 4

m - n = 6 - 4 = 2

a⁶/a⁴ = a²

Now, (a⁶/a⁴) × a⁵ × a⁰ = a² × a⁵ × a⁰

Considering a² × a⁵,

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

a^m × aⁿ = a^{m + n}

Here, m = 2 and n = 5

m + n = 2 + 5 = 7

So, a² × a⁵ = a⁷

Now, (a⁶/a⁴) × a⁵ × a⁰ = a⁷ × a⁰

We know a⁰ = 1

So, a⁷ × a⁰ = a⁷ × 1

= a⁷

Therefore, the exponential form is a⁷.

✦ Try This: Simplify and express the following in exponential form: (2⁵/2³) × 3⁵ × 5⁰

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

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

Summary:

The exponential form of the expression (a⁶/a⁴) × a⁵ × a⁰ is a⁷.

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