Page 74 - Math Course 2 (Book 1)

Monomial Expressions

MO. 3 - L1b Simplify Expressions

Monomials:
Simplifying Expressions Example

Simplify [(8g h ) ] (2gh ) .
3 4 2 2
5 4
Key Concept
[(8g h ) ] (2gh )
5 4
3 4 2 2
Power of a Product = (8g h ) (2gh ) . Power of a Power
3 4 4
5 4
4 4
3 4
4
5 4
4 4
= (8 )(g ) (h ) (2) g (h ) Power of a Product
Words To f nd the power of a product, f nd the
power of each factor and multiply
= 4096g h (16)g h Power of a Power
4 20
12 16
Symbols For any numbers a and b and any
4
20
16
12
m
m m
integer m (ab) = a b . = 4096(16)g • g • h • h Commutative
Property
3 3
3 3 3
3
Example (–2xy) = (–2) x y or –8x y

16 36
= 65,536g h
Answer
Concept Summary Power of Powers
Simplifying Expressions
• To simplify an expression involving monomials, Your Turn!
write an equivalent expression in which:
Express the area as a monomial.
• each base appears exactly once,
• there are no powers of powers, and Express the surface area of 2pq
• all fractions are in simplest form. the cube as a monomial.
3 3
A. 8p q 2pq
B. 24p q 2pq
2 2
Let’s Begin
2 2
C. 6p q
2 2
D. 8p q
Express the area as a monomial.
Answer
Example
Simplify Expressions
2 3 2 3
5 2 3
GEOMETRY Simplify [(2c d ) ] (3c d ) .
Find the volume of a cube with side length 5xyz. A. 1728c d
27 24
Volume = s 3 Formula for volume of a B. 6c d
7 5
cube.
13 10
C. 24c d
3
= (5xyz) Replace s with 5xyz.
7 21
D. 5c d
= 5 x y z Power of a Product
3 3 3 3
Answer
3 3 3
Answer = 125x y z Simplify.

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