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 x 3 x 3 x 3 3

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

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

What is the Exponent? 2 3 x 3 = 3

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

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

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

What is the Base and the Exponent? 9 2

How to Multiply Out an Exponent to Find the Standard Form 4 3 = 3 x 3 x 3 x 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 =

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.

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

Dividing polynomials: Ex: When dividing polynomials, you must divide the coefficients(if possible) and subtract 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.) 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.) p-2 10.) 1/p2 11.)(a2b)0 11.) 1 12.)(x-2y3)-2 12.) x4/y6

13.) p4 p2 13.) p2 14.) 3b2 9b5 14.) 1/3b3 15.) (4x2)2 4x4 15.) 4

16.) x2 * y0 * 32 x3 * y-4 16.) 9y4/x

17.) m 3 * m2n-4 n 17.) m5/n7 18.) 3a2 3 2b-1 b * 32 * a 18.) 6a5/b4

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