Laws of Exponents Objective: Review the laws of exponents for multiplying and dividing monomials.

Laws of Exponents We have learned about seven Laws of Exponents Product of Powers Property When multiplying powers with the same base, add the exponents. am • an = am+n Power of a Power Property When raising a power to another power, multiply the exponents. (am)n = am•n Power of a Product Property When raising a product to a power, raise each term in the product to that power. (a • b)m = am • bm

Laws of Exponents Zero Exponent Property Quotient of Powers Property When dividing powers with the same base, subtract the exponents. = am-n Power of a Quotient Property To find the power of a quotient, find the power of each term and divide. = Zero Exponent Property Any nonzero number raised to the zero power equals one. a0 = 1

Laws of Exponents Negative Exponent Property Any negative exponent is the reciprocal of the positive exponent. a-n = and an =

Examples: (5a2bc3)(1/5 abc4) (-5xy)(4x2)(y4) (10x3yz2)(-2xy5z) (5 ∙ 1/5)(a2 ∙ a1)(b1 ∙ b1)(c3 ∙ c4) a3b2c7 (-5xy)(4x2)(y4) (-5 ∙ 4)(x1 ∙ x2)(y1 ∙ y4) -20x3y5 (10x3yz2)(-2xy5z) (10 ∙ -2)(x3 ∙ x1)(y1 ∙ y5)(z2 ∙ z1) -20x4y6z3 (-2n6y5)(-6n3y2)(ny)3 (-2n6y5)(-6n3y2)(n3y3) (-2 ∙ -6)(n6 ∙ n3 ∙ n3)(y5 ∙ y2 ∙ y3) 12n12y10

Examples: (-3a3n4)(-3a3n)4 -3(2x)4(4x5y)2 . (-3a3n4)(81a12n4) (-3 ∙ 81)(a3 ∙ a12)(n4 ∙ n4) -243a15n8 -3(2x)4(4x5y)2 (-3)(16x4)(16x10y2) (-3 ∙ 16 ∙ 16)(x4 ∙ x10)(y2) -768x14y2 . = (2r)4 = 16r4

Examples: . = n4r4 = 1