# 7.3 Multiplication Properties of Exponents - PowerPoint PPT Presentation

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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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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”

ExamplesNon 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

### 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

• 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

### 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

• 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

• Pg. 464, 18 – 52 Every Other Even

• Pg. 471, 18 – 44 Every Other Even

• Interim Review Due Tuesday