106 algebra De mystif ieD

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

15. (( ))
    ()

x

x

−=

−

8 −^1

8

31

3

16. x
    x

x

x

+

−









= −

+

7 −

23

23

7

1

Properties 7 and 8 allow us to rewrite products and quotients that are raised

to powers.

Property 7 (ab)n = anbn

By Property 7 we can take a product followed by the power or take the powers

followed by the product.

EXAMPLES

Use Property 7 to rewrite the expression.

(4x)^3 = (4x)(4x)(4x) = (4 · 4 · 4)(x  x  x) = 43 x^3 = 64 x^3

[4(x + 1)]^2 = 42 (x + 1)^2 = 16(x + 1)^2

(x^2 y)^4 = (x^2 )^4 y^4 = x^8 y^4

()

()

2 1

2

1

2

1

8

3

x xx (^3333) x
− ===
() 22 ()^1 ()()
2
1
8
13 313
3
xx−−==−−−−xx^13 − =^3
[(5x + 8)^2 (x + 6)]^4 = [(5x + 8)^2 ]^4 (x + 6)^4
= (5x + 8)(2)(4)(x + 6)^4 = (5x + 8)^8 (x + 6)^4
(4x^3 y)^2 = 42 (x^3 )^2 y^2 = 16 x(3)(2)y^2 = 16 x^6 y^2
4(3x)^3 = 4(3^3 x^3 ) = 4(27x^3 ) = 108 x^3
still struggling
It is not true that (a + b)n = an + bn. This mistake is very common.

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EXAMPLES

Use Property 7 to rewrite the expression.

EXAMPLES

Use Property 7 to rewrite the expression.