Exponents 05 – Quotient Law

# Exponents 05 – Quotient Law

• Quotient Law of Exponents

– Variation of Quotient Law

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• 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.

## 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

= 1 .

179

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