Basic Mathematics for College Students

(Nandana) #1

694 Chapter 8 An Introduction to Algebra


Identify the base and the exponent in each expression.
See Example 1.







































Write each expression in an equivalent form using an exponent.
See Example 2.


  1. m m m m  m

  2. r r r r r r









  3. a a b b b

  4. m m m  n  n


Use the product rule for exponents to simplify each expression.
Write the results using exponents.See Example 3.




















  1. (c^5 )(c^8 ) 40. (d^4 )(d^20 )













  2. x^2  y x y^10 46. x^3  y x y^12

  3. m^100  m^100 48. n^600  n^600


cd^4 cd ab^3 ab^4

(a^2 b^3 )(a^3 b^3 ) (u^3 v^5 )(u^4 v^5 )

bb^2 b^3 aa^3 a^5

a^3 a^3 m^7 m^7

53  54 34  36


5 uuu

4 ttttt

 5 u( 5 u)( 5 u)( 5 u)( 5 u)

4 t 4 t 4 t 4 t

(y9)^4 (z2)^3

9 m^12 3.14r^4

 x^4

1


3


y^6

( 3 x)^2 (2xy)^10

a

5


x
b

3
x^5

43 (8)^2


GUIDED PRACTICE


SECTION 8.6 STUDY SET


Fill in the blank.


  1. Expressions such as , and are called
    expressions.

  2. Match each expression with the proper description.


a. Product of exponential expressions with the same
base
b. Power of an exponential expression
c. Power of a product

Fill in the blanks.


  1. a.
    b.

  2. a. b.
    c. d.

  3. To simplify each expression, determine whether you
    add, subtract, multiply, or divide the exponents.
    a.
    b.
    c.

  4. To simplify , what factors within the
    parentheses must be raised to the fourth
    power?


Simplify each expression, if possible.


  1. a. b.

  2. a. b.

  3. a. b.

  4. a. b.


Complete each solution to simplify each expression.
11.


  1. (x^4 )^3 (x^2 )^3
    x^12 x^6
    x


x

x

(x^4 x^2 )^3 ( )^3

NOTATION


42  24 x^3 y^2

x^3 x^2 x^3 x^2

x^2 x x^2 x

x^2 x^2 x^2 x^2

(2y^3 z^2 )^4

(a^4 b^2 )^5

(n^8 )^4

b^6 b^9

(xy)n (ab)c

xx xmxn

( 5 y)( 5 y)( 5 y)

(3x)^4    

CONCEPTS


(a^4 b^2 )^5 (a^8 )^4 a^5 a^3

x^4 , 10^3 (5t)^2

VOCABULARY

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