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7.3 Multiplication Properties of Exponents

7.3 Multiplication Properties of Exponents. Pg. 460. Simplifying Exponential Expressions. There are No Negative Exponents The same base does not appear more than once In a Product or Quotient No Powers are raised to Powers No Products are raised to Powers No Quotients are Raised to Powers

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7.3 Multiplication Properties of Exponents

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  1. 7.3 Multiplication Properties of Exponents Pg. 460

  2. Simplifying Exponential Expressions • There are No Negative Exponents • The same base does not appear more than once • In a Product or Quotient • No Powers are raised to Powers • No Products are raised to Powers • No Quotients are Raised to Powers • Numerical Coefficients in a quotient do not have any common factor other than “1” ExamplesNon Examples

  3. Product of Powers Property • The product of two powers with the same base (Value or Variable) equals that base raised to the sum of the exponents • Rule • If they have the exact (same) base, add the exponents • REMEMBER • Any constant or variable without an exponent, has an exponent with the value of “1” • EXAMPLES

  4. Examples, product of powers

  5. Scientific Notation Example • Light from the sun travels at about 1.86 x 105miles per second. It takes about 500 seconds for the light to reach the earth. Find the Distance from the Sun to the Earth and write answer in Scientific Notation. • We can not multiply as is • We must change 500 to scientific Notation • Then use the distance formula

  6. Power of a Power Property • A Power raised to another power equals that base raised to the product of the exponents • Rule • Remember that if no exponent is written the exponent is “1” • Example

  7. Examples, power of a power

  8. Examples, power of a product

  9. 7.4 Division Properties of Exponents Pg. 467 Quotient of Powers Property Positive Power of a Quotient Property Negative Power of a Quotient Property

  10. Quotient of Powers Property • The quotient of two non-zero powers with the same base equals the base raised to the difference of the exponents • Rule • Example

  11. Examples, quotient of powers property

  12. Dividing Scientific Notation

  13. Positive Powers of a Quotient • A quotient raised to a positive power equals the quotient of each base raised to that power • Examples

  14. Negative Power of a Quotient • A quotient raised to a negative power equals the reciprocal of the quotient raised to the opposite (positive) power • Examples

  15. Homework • 7.3 – 7.4 Book Problems • Pg. 464, 18 – 52 Every Other Even • Pg. 471, 18 – 44 Every Other Even • Interim Review Due Tuesday

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