MathsExponent and PowerExponentsExponents 05 – Quotient Law

Exponents 05 – Quotient Law

Table of Contents

  • 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

    Summary

    = 1 .

    179

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