1. 8.1 Multiplying Monomials
What you’ll learn:
To multiply monomials
To simplify expressions involving powers of monomials

2. Vocab
Monomial – a number, a variable, or the product of a number and one or more variables. NO addition, subtraction or division by a variable!
examples: 6x, 9, -4xy, ¼a²b
not monomials: 5+x, , 3x-8
Constants – monomials with no variable
Recall: 5x³
exponent
coefficient
base

3. Product of Powers
To multiply two powers that have the same base, add the exponents. a⁴a⁵=a⁹ (aaaa)(aaaaa)=a⁹ Remember if there are coefficients to MULTIPLY them DON’T ADD THEM!! Ex: (5x³)(-3x²)=-15x⁵

4. Power of a Power
When an exponent is raised to another power, multiply the exponents. (a²)³=a⁶ (a²)(a²)(a²)=a⁶ (x)⁴=x⁴

5. Power of a Product
To find the power of a product, raise each part to that power. (3x²)⁴=(3⁴)(x²)⁴=81x⁸ (a²b³)³=a⁶b⁹ FYI: A negative number raised to an even power will be positive. A negative number raised to an odd power will be negative.

6. Simplifying Monomial Expressions:
All like-bases are combined.
No powers of powers.
Fractions are simplified.

7. Determine whether each expression is a monomial. Write yes or no.
-53
5x-4y
9-x
5. ⅔x²y³
Yes
No (addition)
No (subtraction)
No (division by a variable)
yes

8. Simplify [(x²)³]² (x⁶)² (xy²)(x³y) (3x²y)²(2x⁴y³)³ x⁴y³ (-5x⁴)² 25x⁸
(2a²b³c⁴)(-5ab²c²)
-10a³b⁵c⁶ 4.

9. Homework p even