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Rules of Exponents

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The document discusses eight laws of exponents: 1) The exponent indicates how many times the base is multiplied by itself. 2) If the bases are the same and the operation is multiplication, the exponent is the sum of the individual exponents. 3) If the bases are the same and the operation is division, the exponent is the difference of the individual exponents. 4) If an exponential form is raised to another exponent, the result is the base raised to the product of the exponents.

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ExponentsExponents { 3 5power base exponent 3 3 means that is the exponential form of t Example: he number 125 5 5 .125 =
The Laws of Exponents:The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiply itself. n n times x x x x x x x x − = × × ×××× × × ×144424443 3 Example: 5 5 5 5= × ×
The Laws of Exponents:The Laws of Exponents: #2: Multiplicative Law of Exponents: If the bases are the same And if the operations between the bases is multiplication, then the result is the base powered by the sum of individual exponents . m n m n x x x + × = 3 4 3 4 7 Example: 2 2 2 2+ × = = ( ) ( )3 4 7 Proof: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 × = × × × × × × = × × × × × × =
The Laws of Exponents:The Laws of Exponents: #3: Division Law of Exponents: If the bases are the same And if the operations between the bases is division, then the result is the base powered by the difference of individual exponents . m m n m n n x x x x x − = ÷ = 4 4 3 4 3 1 3 5 Example: 5 5 5 5 5 5 − = ÷ = = = 4 3 5 5 5 5 5 Proof: 5 5 5 5 5 × × ×/ = = × ×/
The Laws of Exponents:The Laws of Exponents: #4: Exponential Law of Exponents: If the exponential form is powered by another exponent, then the result is the base powered by the product of individual exponents. ( ) nm mn x x= ( ) 23 3 2 6 Example: 4 4 4× = = ( ) ( ) ( ) ( ) 2 23 6 Proof: 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 = × × = × × × × × = = × × × × × =
The Laws of Exponents:The Laws of Exponents: #5: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent. ( ) n n n xy x y= × ( ) 22 2 2 2 2 Proof: 2 3 4 9 Example: 36 6 2 3 2 3 36 = = × = × × = × =
The Laws of Exponents:The Laws of Exponents: #6: Quotient Law of Exponents: If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent. n n n x x y y   = ÷   3 3 3 2 2 Example: 7 7   = ÷  
The Laws of Exponents:The Laws of Exponents: #7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. 1m m x x − = 3 3 1 1 Example #1: 2 2 8 − = = 3 3 3 1 5 Example #2: 5 125 5 1− = = =
The Laws of Exponents:The Laws of Exponents: #8: Zero Law of Exponents: Any base powered by zero exponent equals one 0 1x = ( ) 0 0 0 Example: 112 1 5 1 7 1flower =   = ÷   =
The Laws of Exponents:The Laws of Exponents: #8: Zero Law of Exponents: Any base powered by zero exponent equals one 0 1x = ( ) 0 0 0 Example: 112 1 5 1 7 1flower =   = ÷   =

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Rules of Exponents

  • 1. ExponentsExponents { 3 5power base exponent 3 3 means that is the exponential form of t Example: he number 125 5 5 .125 =
  • 2. The Laws of Exponents:The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiply itself. n n times x x x x x x x x − = × × ×××× × × ×144424443 3 Example: 5 5 5 5= × ×
  • 3. The Laws of Exponents:The Laws of Exponents: #2: Multiplicative Law of Exponents: If the bases are the same And if the operations between the bases is multiplication, then the result is the base powered by the sum of individual exponents . m n m n x x x + × = 3 4 3 4 7 Example: 2 2 2 2+ × = = ( ) ( )3 4 7 Proof: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 × = × × × × × × = × × × × × × =
  • 4. The Laws of Exponents:The Laws of Exponents: #3: Division Law of Exponents: If the bases are the same And if the operations between the bases is division, then the result is the base powered by the difference of individual exponents . m m n m n n x x x x x − = ÷ = 4 4 3 4 3 1 3 5 Example: 5 5 5 5 5 5 − = ÷ = = = 4 3 5 5 5 5 5 Proof: 5 5 5 5 5 × × ×/ = = × ×/
  • 5. The Laws of Exponents:The Laws of Exponents: #4: Exponential Law of Exponents: If the exponential form is powered by another exponent, then the result is the base powered by the product of individual exponents. ( ) nm mn x x= ( ) 23 3 2 6 Example: 4 4 4× = = ( ) ( ) ( ) ( ) 2 23 6 Proof: 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 = × × = × × × × × = = × × × × × =
  • 6. The Laws of Exponents:The Laws of Exponents: #5: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent. ( ) n n n xy x y= × ( ) 22 2 2 2 2 Proof: 2 3 4 9 Example: 36 6 2 3 2 3 36 = = × = × × = × =
  • 7. The Laws of Exponents:The Laws of Exponents: #6: Quotient Law of Exponents: If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent. n n n x x y y   = ÷   3 3 3 2 2 Example: 7 7   = ÷  
  • 8. The Laws of Exponents:The Laws of Exponents: #7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. 1m m x x − = 3 3 1 1 Example #1: 2 2 8 − = = 3 3 3 1 5 Example #2: 5 125 5 1− = = =
  • 9. The Laws of Exponents:The Laws of Exponents: #8: Zero Law of Exponents: Any base powered by zero exponent equals one 0 1x = ( ) 0 0 0 Example: 112 1 5 1 7 1flower =   = ÷   =
  • 10. The Laws of Exponents:The Laws of Exponents: #8: Zero Law of Exponents: Any base powered by zero exponent equals one 0 1x = ( ) 0 0 0 Example: 112 1 5 1 7 1flower =   = ÷   =