# 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 Numerical Coefficients in a quotient do not have any common factor other than “1” Examples Non Examples

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

Examples, product of powers

Scientific Notation Example
Light from the sun travels at about 1.86 x 105 miles 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
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

Examples, power of a power

Examples, power of a product

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

Examples, quotient of powers property

Dividing Scientific Notation

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

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