Exponents 05 – Quotient Law | Class 7 Maths Exponent and Power

Table of Contents

• Quotient Law of Exponents

– Variation of Quotient Law

• Problems
• Summary
• What’s Next?

In the previous segment, we learnt about the Product law of exponents. In this segment, we will learn about the Quotient law of exponents. Get R D Sharma Maths Class 7 Solutions

What is the Quotient law of exponents?

The Quotient law of exponents states that,

For any non-zero integer a, ?^? ÷ ?^? = ?^?−?, where m and n are whole numbers and m > n.

For example,

3⁵ ÷ 3³ = 3⁵⁻³ = 3².

This law applies to only the division of exponential forms with the same base.

Variation of quotient law when m < n

For any non-zero integer a, ?^? ÷ ?^? = 1

??−?

, where m and n are whole numbers and m < n.

For example,

3³ ÷ 3⁵ = 1

35−3

1

= 32

Problems based on quotient law

Q. Express ?^? ÷ ?^? in exponential form. Solution:

The bases are the same and m > n. Thus applying the quotient law, 6⁹ ÷ 6³ = 6⁹⁻³ = 6⁶.

Q. Express ??^?? ÷ ??^?? in exponential form. Solution:

The bases are the same, but m < n. Thus, applying the variation of the quotient law, 17¹² ÷

17²¹ = 1

1721−12

Summary

= 1 .

179