Exponents

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

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

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

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

How to read an Exponent This exponent is read three to the 2nd power or three squared. It can also be read 3 times itself twice. 3 2 Exponent Base

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

What is the Exponent? 3 2 ∙ 2 ∙ 2 = 2

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

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

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

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

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

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

What is the Base and Exponent in Standard Form? 2 3 9 =

What is the Base and Exponent in Standard Form? 3 5 125 =

Exponents use patterns 4³ is 4 ∙ 4 ∙ 4 = 64 4 times itself 3 times 4² is 4 ∙ 4 = 16 or 4 times itself 2 times 4 ¹ is 4 = 4 or 4 times itself just once do you see the pattern? Let’s consider what would 4º How could we get from 16 to 4? What would we get when we do the same to 4

Now let’s try negative exponents We will follow the same pattern 4³ = 64 4 ∙4 ∙4 4² = 16 4 ∙4  64 ÷4 4¹ = 4 16÷4 4º = 1 4÷4 What do you think 4-1 1÷4 4-1 = 1/4

There are many types of exponent laws... Negative exponent law. Quotient Law. The Zero exponent law. There's a product law. And last but not least... Power of a power.

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

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

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

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

Negative exponents: Ex: To make an exponent positive, flip the base. NOTE: This does not change the sign of the base. This is also a division problem (patterns) Remember 8¹=8 8º= 1 (8÷8) 8-1 = 1÷8 = 1/8 8-2 = 1/8 ÷ 8 = 1/64

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

Please simplify the following equations: How?: Answer:

Please simplify the following equations: How?: Answer:

Please simplify the following equations: How?: Answer:

Please simplify the following equations: How?: Answer:

Please simplify the following equations: How?: Answer:

Please simplify the following equations: How?: Answer:

Review

Copy and complete each of the following questions.

1.) 4³ 2.) (2+3)² 3.) 10º 4.) 5-1 5.) 6-2 next we will try some written with variables. – Ready for a challenge? 

1.) b2 * b7 1.) b9 2.) (p3)4 2.) p12 3.) (a2)3 * a3 3.) a9 4.) x2 * (xy)2 4.) x4y2 5.) (4m)2 * m3 5.) 16m5 6.) (3a)3*(2p)2 6.) 108a3p2

7.)82*(xy)2*2x 7.) 128x3y2 8.) w3 * (3w)4 8.) 81w7 9.) q0 9.) 1 10.)(a2b)0 10.) 1