7 3 multiplication properties of exponents
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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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Simplifying exponential expressions
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


Product of powers property
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



Scientific notation example
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


Power of a power property
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 4 division properties of exponents

7.4 Division Properties of Exponents

Pg. 467

Quotient of Powers Property

Positive Power of a Quotient Property

Negative Power of a Quotient Property


Quotient of powers property
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




Positive powers of a quotient
Positive Powers of a Quotient

  • A quotient raised to a positive power equals the quotient of each base raised to that power

  • Examples


Negative power of a quotient
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


Homework
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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