7.1 Multiplication Properties of Exponents NOTES

Monomial: a number, variable, or the product of a number and one or more variables with nonnegative integer exponents Constant: A monomial that is a real number

Not a monomial 2𝑥 has a variable as an exponent

𝑥2 + 3 a sum (can’t have addition/subtraction)

5𝑎−2 can’t have negative exponents 3𝑥 a quotient

Determine whether each expression is a monomial or not a monomial.

1) 10 2) 𝑓 + 24 3) ℎ2

4) J 5) 23𝑎𝑏𝑐𝑑2 6) 𝑚𝑝𝑛

To multiply two powers that have the same base, ADD their exponents.

Example: 𝒃𝟑 ∙ 𝒃𝟓 = 𝒃𝟑+𝟓 = 𝒃𝟖 the base in this example is b

Simplify each expression.

7) (6𝑛3)(2𝑛7) 8) (3𝑝𝑡3)(𝑝3𝑡4) 9) (𝑟4)(−12𝑟7)

Monomial -4 a number

Y a variable

𝑎2 the product of variables 12 𝑥2𝑦 the product of numbers and variables

7.1 Multiplication Properties of Exponents NOTES

To find a power of a power, multiply the exponents.

Example: (𝒃𝟑)𝟓 = 𝒃𝟑∙𝟓 = 𝒃𝟏𝟓

Simplify each expression.

10) (32)4 11) (𝑟4)3

To find the power of a product, find the power of each factor and multiply.

Example: (−𝟐𝒙𝒚𝟑)𝟓 = −𝟐𝟏∙𝟓𝒙𝟏∙𝟓𝒚𝟑∙𝟓 = −𝟑𝟐𝒙𝟓𝒚𝟏𝟓

Simplify each expression.

12) [(23)2]4 13) [(22)2]4

14) (3𝑥𝑦4)2[(−2𝑦)2]3 15) (12 𝑎2𝑏2)

2 [(−4𝑏)2]2