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Product Rule

The document outlines six rules for exponents: 1) The product rule which states to add exponents when multiplying the same base. 2) The quotient rule which states to subtract exponents when dividing the same base. 3) The zero exponent rule where any base raised to the zero power is equal to one. 4) The power rule which states to multiply exponents when raising a power to another power. 5) The expanded power rule which also multiplies exponents when raising a term with multiple bases to a power. 6) The negative exponent rule where changing the sign of the exponent occurs when moving a factor with an exponent across a fraction bar. Examples are provided to illustrate each rule.

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Jason Oh
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60 views2 pages

Product Rule

The document outlines six rules for exponents: 1) The product rule which states to add exponents when multiplying the same base. 2) The quotient rule which states to subtract exponents when dividing the same base. 3) The zero exponent rule where any base raised to the zero power is equal to one. 4) The power rule which states to multiply exponents when raising a power to another power. 5) The expanded power rule which also multiplies exponents when raising a term with multiple bases to a power. 6) The negative exponent rule where changing the sign of the exponent occurs when moving a factor with an exponent across a fraction bar. Examples are provided to illustrate each rule.

Uploaded by

Jason Oh
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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1.

PRODUCT RULE:
To multiply when two bases are the same, write
the base and ADD the exponents.

Example:

𝒙𝟑 ∙ 𝒙𝟖 = 𝒙𝟏𝟏

2. QUOTIENT RULE:
To divide when two bases are the same, write the
base and SUBTRACT the exponents.
𝒙𝒎 𝒎−𝒏
=𝒙
𝒙𝒏
Example:
𝒙𝟓
= 𝒙𝟑
𝒙𝟐

3. ZERO EXPONENT RULE:


Any base (except 0) raised to the zero powder is
equal to one.

Example:

𝒚𝟎 = 𝟏

Example:

𝒙𝟐 𝟒 (𝒙𝟐 )𝟒 𝒙𝟖
( ) = = 𝒚𝟒
𝒚 𝒚𝟒
4. POWER RULE:
To raise a power to another power, write the base
and MULTIPLY the exponents.

(𝒙𝒎 )𝒏 = 𝒙𝒎∙𝒏
Example:

(𝒙𝟑 )𝟐 = 𝒙𝟔

5. EXPANDED POWER RULE:


When raising a power to a power, you MULTIPLY
the exponents.

(𝒙𝒚)𝒎 = 𝒙𝒎 𝒚𝒏
Example:

(𝟐𝒂)𝟑 = 𝟐𝟑 𝒂𝟑 = 𝟖𝒂𝟑

6. NEGATIVE EXPONENTS:
If a factor in the numerator or denominator is
moved across the fraction bar, the sign of the exponent
is changed.
𝟏
𝒙−𝒎 = 𝒎
𝒙

Example:
𝟏
𝒙−𝟑 = 𝒙𝟑
𝟏
= 𝒙𝒎
𝒙−𝒎
Example:
𝒂−𝟐 𝒃𝟑
𝒄−𝟒 𝒅−𝟏

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