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7.3 Multiplication Properties of Exponents

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7.3 Multiplication Properties of Exponents

Pg. 460

- 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

- 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

- REMEMBER

- 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

- We can not multiply as is

- 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

Pg. 467

Quotient of Powers Property

Positive Power of a Quotient Property

Negative Power of a Quotient Property

- The quotient of two non-zero powers with the same base equals the base raised to the difference of the exponents
- Rule
- Example

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

- A quotient raised to a negative power equals the reciprocal of the quotient raised to the opposite (positive) power
- Examples

- 7.3 – 7.4 Book Problems
- Pg. 464, 18 – 52 Every Other Even
- Pg. 471, 18 – 44 Every Other Even

- Interim Review Due Tuesday