Properties of Exponents Advanced Math Topics Mrs Mongold

Properties of Exponents Advanced Math Topics Mrs. Mongold

Take a Piece of Paper and fold it in 4 to make a Frayer Organizer l Center on both sides is Exponent Properties

1. Negative Exponents l For any real number a = 0 and any integer n, a-n =

2. Product of Powers l For any real number a and integers m and n, am · an = am+n

3. Quotient of Powers l For any real number a = 0, and any integers m and n, = am - n

4. Power to a Power l Mulitply exponents when you have a power to a power , (am)n = amn

5. Power of a Product l Distribute the exponent when you have a power of a product (ab)m = ambm

6. Power of a Quotient l Take the numerator and denominator to the power outside,

7. Zero Power l Any number raised to the 0 power is 1

8. Fractional Exponents l A fractional exponent turns into a radical

Fractional Exponents l

Fractional Exponents l

Examples l 42 ∙ 4 3

Examples l 42 ∙ 43 =45 = 1024

Examples l 42 ∙ 43 =45 = 1024 l -3 y ∙ -9 y 4

Examples l 42 ∙ 43 =45 = 1024 l -3 y ∙ -9 y 4 = 27 y 5 l (-4 x 3 p 2)(4 y 3 x 3)

Examples l 42 ∙ 43 =45 = 1024 l -3 y ∙ -9 y 4 = 27 y 5 l l (-4 x 3 p 2)(4 y 3 x 3) = -16 x 6 y 3 p 2

Examples l 42 ∙ 43 =45 = 1024 l -3 y ∙ -9 y 4 = 27 y 5 l l (-4 x 3 p 2)(4 y 3 x 3) = -16 x 6 y 3 p 2 -80

Examples l 42 ∙ 43 =45 = 1024 l -3 y ∙ -9 y 4 = 27 y 5 l l (-4 x 3 p 2)(4 y 3 x 3) = -16 x 6 y 3 p 2 -80 = -1

l (5 x)0 + 5 x 0

l (5 x)0 + 5 x 0 = 1 + 5 = 6

l x 9 y 6 x 8 y 6

l x 9 y 6 x 8 y 6 =x

-36 a 5 b 7 c 10 6 ab 3 c 4

-36 a 5 b 7 c 10 4 b 7 c 6 = -6 a 6 ab 3 c 4

l 8 r 4 2 r-4 l y-7 y y 8 4 x 0 + 5 l

l l l 8 r 4 2 r-4 =4 r 8 y-7 y y 8 4 x 0 + 5 = 9

l -3 z 4 ∙ 10 z 7 l (4 x)-1 l 30 – 3 t 0

l

l l x-7 y-2 x 2 y 2 (24 x 8)(x) 20 x-7

l l x-7 y-2 x 2 y 2 (24 x 8)(x) 20 x-7

Examples l Write each fractional exponent as a radical

Homework l Worksheet 1 & 2