Bell Ringer Solve. 1. 6x – 8 = -4x + 22 + 8 + 8 2x = 30 2 2 x = 15 2. -3(x – 6)= 3 -3x + 18 = 3 – 18 – 18 -3x = -15 -3 -3 x = 5

Homework 1296 -1296 1/27 4096 1 1/125 -128 16 80 512 3/16 x3 y4 15x12 1/c9 n4 4x6y5 7y2/x3 3 1728 2x 2x2 -4/y2 5y/x2 2y2/x5 3x7/y2 6x2/y3z3

Laws of Exponents, Pt. I Review! Zero Exponent Property Negative Exponent Property Product of Powers Quotient of Powers

Laws of Exponents, Pt. 1 x0 = 1 30 = 1 120 = 1 x-1 = 5-3 = 3x2y-3 = 1 Zero Exponent Property – Any number raised to the zero power is 1. x0 = 1 30 = 1 120 = 1 Negative Exponent Property – Any number raised to a negative exponent is the reciprocal of the number. x-1 = 5-3 = 3x2y-3 = 1 x 1 53 3x2 y3

Laws of Exponents, Pt. 1 x2•x8 = x10 3x4•x-2 = 3x2 x6 x2 10x4y3 2x7y Product of Powers – When multiplying numbers with the same bases, ADD the exponents. Quotient of Powers – When dividing numbers with the same bases, SUBTRACT the exponents. x2•x8 = x10 3x4•x-2 = 3x2 x6 x2 10x4y3 2x7y 5y2 x3 = x4 =

Solve the problem in pieces. Bonus! Solve the problem in pieces. 30 x6 y2 z5 6 x3 y5 z8 5x3 y3z3 = 1. Whole numbers 2. x 3. y 4. z 10 x2 z6 15 x5 y3 2z6 3x3y3 =

Power of a Power Power of a Product Power of a Quotient Laws of Exponents, Pt. II Power of a Power Power of a Product Power of a Quotient

Power of a Power (63)4 = 63•63•63•63 = 612 (x5)3 = x5•x5•x5 = x15 This property is used to write an exponential expression as a single power of the base. (63)4 = 63•63•63•63 = 612 (x5)3 = x5•x5•x5 = x15 When you have an exponent raised to an exponent, multiply the exponents!

Multiply the exponents! Power of a Power (54)8 = 532 Multiply the exponents! (n3)4 = n12 (3-2)-3 = 36 1 x15 (x5)-3 = x-15 =

Power of a Product (xy)3 (2x)5 = x3y3 = 25 ∙ x5 = 32x5 (xyz)4 Power of a Product – Distribute the exponent on the outside of the parentheses to all of the terms inside of the parentheses. (xy)3 (2x)5 = x3y3 = 25 ∙ x5 = 32x5 (xyz)4 = x4 y4 z4

Power of a Product (x3y2)3 (3x2)4 = x9y6 = 34 ∙ x8 = 81x8 (3xy)2 More examples… (x3y2)3 (3x2)4 = x9y6 = 34 ∙ x8 = 81x8 (3xy)2 = 32 ∙ x2 ∙ y2 = 9x2y2

( ) ( ) x x5 = y y5 Power of a Quotient Power of a Quotient – Distribute the exponent on the outside of the parentheses to the numerator and the denominator of the fraction. ( ) ( ) x y 5 x5 y5 =

( ) ( ) ( ) ( ) 2 x 23 x3 8 x3 = = 3 x2y 34 x8y4 81 x8y4 = = Power of a Quotient More examples… ( ) ( ) 2 x 3 23 x3 8 x3 = = ( ) ( 3 x2y ) 4 34 x8y4 81 x8y4 = =

Basic Examples

Basic Examples

Basic Examples

More Difficult Examples

More Examples

More Examples