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Exponents

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Location of Exponent An exponent is a little number high and to the right of a regular or base number. 3 4 Base Exponent

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Definition of Exponent An exponent tells how many times a number is multiplied by itself. 3 4 Base Exponent

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What an Exponent Represents An exponent tells how many times a number is multiplied by itself. 3 4 = 3 x 3 x 3 x 3

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How to read an Exponent This exponent is read three to the fourth power. 3 4 Base Exponent

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How to read an Exponent This exponent is read three to the 2 nd power or three squared. 3 2 Base Exponent

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How to read an Exponent This exponent is read three to the 3rd power or three cubed. 3 3 Base Exponent

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What is the Exponent? 2 x 2 x 2 =2 3

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What is the Exponent? 3 x 3 =3 2

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What is the Exponent? 5 x 5 x 5 x 5 =5 4

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What is the Base and the Exponent? 8 x 8 x 8 x 8 =8 4

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What is the Base and the Exponent? 7 x 7 x 7 x 7 x 7 =7 5

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What is the Base and the Exponent? 9 x 9 =9 2

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How to Multiply Out an Exponent to Find the Standard Form = 3 x 3 x 3 x 33 9 27 81 4

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What is the Base and Exponent in Standard Form? 4 2 = 16

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What is the Base and Exponent in Standard Form? 2 3 = 8

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3 2 = 9

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5 3 = 125

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Product law: add the exponents together when multiplying the powers with the same base. Ex: NOTE: This operation can only be done if the base is the same!

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Quotient law subtract the exponents when dividing the powers with the same base. Ex: NOTE: This operation can only be done if the base is the same!

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Power of a power: keep the base and multiply the exponents. Ex: NOTE: Multiply the exponents, not add them!

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Zero exponent law: Any power raised to an exponent of zero equals one. Ex: NOTE: No matter how big the number is, as long as it has zero as an exponent, it equals to one. Except

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Negative exponents: To make an exponent positive, flip the base. Ex: NOTE: This does not change the sign of the base.

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Multiplying Polynomials: In multiplying polynomials, you have to multiply the coefficients and add up the exponents of the variables with the same base. Ex:

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Dividing polynomials: When dividing polynomials, you must divide the coefficients(if possible) and subtract the exponents of the variables with the same base. Ex:

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Please simplify the following equations: Answer: How?:

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Please simplify the following equations: Answer: How?:

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Please simplify the following equations: Answer: How?:

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Please simplify the following equations: Answer: How?:

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Please simplify the following equations: Answer: How?:

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Please simplify the following equations: Answer: How?:

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Review

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Copy and complete each of the following questions.

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1.) b 2 * b 7 1.) b 9 2.) (p 3 ) 4 2.) p 12 3.) (a 2 ) 3 * a 3 3.) a 9 4.) x 2 * (xy) 2 4.) x 4 y 2 5.) (4m) 2 * m 3 5.) 16m 5 6.) (3a) 3 *(2p) 2 6.) 108a 3 p 2

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7.)8 2 *(xy) 2 *2x 7.) 128x 3 y 2 8.) w 3 * (3w) 4 8.) 81w 7 9.) q 0 9.) 1 10.) p -2 10.) 1/p 2 11.)(a 2 b) 0 11.) 1 12.)(x -2 y 3 ) -2 12.) x 4 /y 6

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13.) p 4 p 2 13.) p 2 14.) 3b 2 9b 5 14.) 1/3b 3 15.) (4x 2 ) 2 4x 4 15.) 4

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16.) x 2 * y 0 * 3 2 x 3 * y -4 16.) 9y 4 /x

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17.) m 3 * m 2 n -4 n 17.) m 5 /n 7 18.) 3a 2 3 2b -1 b * 3 2 * a 18.) 6a 5 /b 4

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19) (3/4) 3 19) 27/64 20) 2+3(4) 2 20) 50

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