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

2. 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

3. 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

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

5. 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

6. 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

7. Examples: .
= n4r4
= 1