2 Contents Multiplication Properties of Exponents ……….1 – 13 Zero Exponent and Negative Exponents……14 – 24Division Properties of Exponents ……………….15 – 32Simplifying Expressions using Multiplication and Division Properties of Exponents…………………33 – 51Scientific Notation ………………………………………
3 Multiplication Properties of Exponents Product of Powers PropertyPower of a Power PropertyPower of a Product Property
4 Product of Powers Property To multiply powers that have the same base, you add the exponents.Example:
13 Review Multiplication Properties of Exponents Product of Powers Property—To multiply powers that have the same base, ADD the exponents.Power of a Power Property—To find a power of a power, multiply the exponents.Power of a Product Property—To find a power of a product, find the power of each factor and multiply.
14 Zero Exponents Any number, besides zero, to the zero power is 1. Example:
15 Negative ExponentsTo make a negative exponent a positive exponent, write it as its reciprocal.In other words, when faced with a negative exponent—make it happy by “flipping” it.
16 Negative Exponent Examples Example of Negative Exponent in the Numerator:The negative exponent is in the numerator—to make it positive, I “flipped” it to the denominator.
17 Negative Exponents Example Negative Exponent in the Denominator:The negative exponent is in the denominator, so I “flipped” it to the numerator to make the exponent positive.
18 Practice Making Negative Exponents Positive Try:
20 Rewrite the Expression with Positive Exponents Example:Look at EACH factor and decide if the factor belongs in the numerator or denominator.All three factors are in the numerator. The 2 has a positive exponent, so it remains in the numerator, the x has a negative exponent, so we “flip” it to the denominator. The y has a negative exponent, so we “flip” it to the denominator.
21 Rewrite the Expression with Positive Exponents Example:All the factors are in the numerator. Now look at each factor and decide if the exponent is positive or negative. If the exponent is negative, we will flip the factor to make the exponent positive.
22 Rewriting the Expression with Positive Exponents Example:The 4 has a negative exponent so to make the exponent positive—flip it to the denominator.The exponent of a is 1, and the exponent of b is 3—both positive exponents, so they will remain in the numerator.The exponent of c is negative so we will flip c from the numerator to the denominator to make the exponent positive.
23 Practice Rewriting the Expressions with Positive Exponents: Try:
34 Steps to Simplifying Expressions Power of a Quotient Property along with Power of a Power Property to remove parenthesis“Flip” negative exponents to make them positive exponentsUse Product of Powers PropertyUse the Quotient of Powers Property
35 Power of a Quotient Property and Power of a Power Property Use the power of a quotient property to remove parenthesis and since the expression has a power to a power, use the power of a power property.
56 Write a Number in Scientific Notation To write a number in scientific notation, move the decimal to make a number between 1 and 9. Multiply by 10 and write the exponent as the number of places you moved the decimal.A positive exponent represents a number larger than 1 and a negative exponent represents a number smaller than 1.
57 Example of Writing a Number in Scientific Notation Write 88,000,000 in scientific notationFirst place the decimal to make a number between 1 and 9.Count the number of places you moved the decimal.Write the number as a product of the decimal and 10 with an exponent that represents the number of decimal places you moved.Positive exponent represents a number larger than 1.
58 Write 0.0422 in Scientific Notation Move the decimal to make a number between 1 and 9 – between the 4 and 2Write the number as a product of the number you made and 10 to a power 4.2 X 10Now the exponent represents the number of places you moved the decimal, we moved the decimal 2 times. Since the number is less than 1 the exponent is negative.
59 Operations with Scientific Notation For example:Multiply 2.3 and 1.8 = 4.14Use the product of powers propertyWrite in scientific notation