PROPERTIES of EXPONENTS

3 Location of Exponent 4 Exponent Base 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

Properties

MULTIPLYING POWERS WITH THE SAME BASE Words Numbers Algebra To multiply powers with the same base, keep the base and add the exponents. bm • bn = bm + n 35 • 38 = 35 + 8 = 313 MULTIPLYING POWERS WITH THE SAME BASE

Together! Alone! 1. 66 • 63 1. 42 • 44 2. x2 • x3 2. n5 • n7 3. x5 • y2 3. 25 • 2 4. 412 • 417 4. 244 • 244

Multiplying Power of a Power Words Numbers Algebra To multiply power of a power, keep the base and multiply the exponents. Multiplying Power of a Power (pr)s = pr • s NOTE: Multiply the exponents, not add them!

1. (y4)2 1. (x2)3 2. (55)2 3. (3²)⁴ 4. (4)² 2. (3)6 3. (2⁶)² 4. (6²)³ Together! Alone! 1. (y4)2 1. (x2)3 2. (55)2 3. (3²)⁴ 4. (4)² 2. (3)6 3. (2⁶)² 4. (6²)³

Power of a Product (a · b)ᴹ = aᴹ · bᴹ Example (5 · 7)² = 5² · 7² To raise a product to a power, raise each factor to the power Example (5 · 7)² = 5² · 7² (4x)³ = 4³ · x³

1. (3y)2 1. (7x)3 2. (5 · 3)2 3. (3²x³)⁴ 4. 3² · 5² 2. (3 · 2)6 Together! Alone! 1. (3y)2 1. (7x)3 2. (5 · 3)2 3. (3²x³)⁴ 4. 3² · 5² 2. (3 · 2)6 3. (2⁶x)² 4. 4³ · 2³

1.) b2 • b7 2.) (p3)4 3.) (a2)3 • a3 4.) x2 • (xy)2 5.) (4m)2 • m3 6.) (3a)3 •(2p)2 7.) w3 • (3w)4 8.) 7² · 3² 9.) (3² x³)⁴ 10.)(x2y3)2 Pair- Practice!

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:

Division Properties of Exponents

Finding Quotients of Powers Simplify Alone Together A. A. B. B. C. C. D. D.

Finding Positive Powers of Quotient Simplify. Alone Together A. A. B. B. C. C.

Remember that What if x is a fraction?

Finding Negative Powers of Quotients Simplify. Alone Together A. A. B. B. C. C.