1. Multiplication of Monomials
Chapter 7.2

2. Recall when a number is raised to a power the number is the base and the exponent is the power.
23: 2 is the base and 3 is the exponent.
Variables can be raised to powers also.
x5 : x is the base and 5 is the exponent.

3. Rule for Multiplying exponential Expressions
If m and n are integers then,
(xm)(xn)= x(m+n)

4. Examples with one Variable
(x2)( x3)= x(2+3) = x5
(x4 )( x5)= x(4+5) = x9
(x)( x7)= x(1+7) = x8
If a variable does not have an exponent it is assumed to be raised to the power of 1.

5. Examples With Numerous Variables
(3x2 )(6x3)
= (3)(6)(x2 x3)=18 x(2+3) = 18x5
(-3xy2)(-4x2y3)
=(-3)(-4)(xx2)(y2y3)) =12x3 y5
(-x2y3)(11x9)
=(-1)(11)(x2 x9)(y3) = -11x11y3

6. Simplify Monomials Raised to Powers.
Rule for simplifying Powers of Exponential Expressions.
(xm)n = xmn ; Just multiply the exponents.
Rule for simplifying Powers of Products.
(xmyn)p = xmp ynp Just multiply the exponents.

7. Examples of Exponential Powers
x2*5 = x10
2. (x2y5)5 =
x2*5y5*5 = x10 y25
3. (3x2y5)3 =
(3)3 (x2)3( y5)3 = 27 x6y15

8. Examples: Recall PEMDAS
1. (-2x) (-3xy2)3 =
(-2x)(-3)3 (x)3 (y2)3 = (-2)(-27) (xx3) (y6) =
54x4 y6
2. (3x) (2x2y2)3 =(3x) (2)3(x2)3(y2)3 =
(3*8)(xx6)(y6) =
24x7 y6

9. YOU TRY! 1. (x9)5 2. (x2)15 3. (x2y8)5 4. (4x2y3)3 5. (3xy2)(-2x2y5)5

10. Answers
1. x45
2. x30
3. x10 y40
4. 64x6y9
x11y27
6. -32x12y10