Properties of Exponents

Properties of Exponents Advanced Math Topics Mrs. Mongold

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

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

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

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

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

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

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

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

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

Fractional Exponents

Examples • 42 ∙ 43

Examples • 42 ∙ 43 =45 = 1024

Examples • 42 ∙ 43 =45 = 1024 • -3y ∙ -9y4

Examples • 42 ∙ 43 =45 = 1024 • -3y ∙ -9y4 = 27y5 • (-4x3p2)(4y3x3)

Examples • 42 ∙ 43 =45 = 1024 • -3y ∙ -9y4 = 27y5 • (-4x3p2)(4y3x3) = -16x6y3p2

Examples • 42 ∙ 43 =45 = 1024 • -3y ∙ -9y4 = 27y5 • (-4x3p2)(4y3x3) = -16x6y3p2 • -80

Examples • 42 ∙ 43 =45 = 1024 • -3y ∙ -9y4 = 27y5 • (-4x3p2)(4y3x3) = -16x6y3p2 • -80 = -1

(5x)0 + 5x0

(5x)0 + 5x0 = 1 + 5 = 6

x9y6 x8y6

x9y6 x8y6 =x

-36a5b7c10 6ab3c4

-36a5b7c10 6ab3c4 = -6a4b7c6

8r4 2r-4 • y-7y y8 • 4x0 + 5

8r4 2r-4 • y-7y y8 • 4x0 + 5 = 9 =4r8

-3z4∙ 10z7 • (4x)-1 • 30 – 3t0

x-7y-2 x2y2 • (24x8)(x) 20x-7

Examples • Write each fractional exponent as a radical

Homework • Worksheet 1 & 2

Properties of Exponents