Page 266 - Algebra 1

Power of a Quotient Property
If x and y are any nonzero real numbers and m is an integer, then
_xm _xm (y) = ym.
Example
4
Simplifying a Power of a Quotient
Simplify each expression.
_2 _24
a. (2x) 5
b. (-x ) 3y3
SOLUTION
SOLUTION
2x 2 -x
_ _24
_) (-1)4(x2)4
The rules for exponents apply to many expressions with powers. When simplifying expressions, be sure to follow the order of operations.
Simplifying Expressions with Powers
3 () (3y
5_
= 22x2 2=
5_ _2 8 x
=4x = 12 25 81y
434 (3) (y )
Example
5
Simplify each expression.
a. (4xy2)2(2x3y)2 SOLUTION
(4xy2)2(2x3y)2
= (42x2y4)(22x6y2) = (16x2y4)(4x6y2) = 64x8y6
Simplify each expression.
Math Reasoning
Justify Is 5(x2)3 equivalent to (5x2)3 ? Justify your answer.
a.
(Ex 1)
c.
(Ex 2)
e.
(Ex 4)
g.
(Ex 3)
(52)2 (-3n4)2
b. (-5x-2)2(3xy2)4 SOLUTION
(-5x-2)2(3xy2)4
= (-52x-4)(34x4y8) = (25x-4)(81x4y8) = 2025x0y8
= 2025y8
b. (b4)7 (Ex 1)
d. (9ab-2)2(2a2b4) (Ex5) _
f. (-x)2 (Ex 4) 7y5
A shipping container is in the shape of a cube with a side length of 3x inches. What is the volume of the container?
Lesson Practice
_4 3
(3y ) 4
Lesson 40 251