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Exponents and Their Properties - Multiplying and Dividing Monomials Algebra 1

When we want to express a product of the same number like 3 3 3 3 we can use a shortcut notation

exponent

34

base

The exponent tells how many times the base is used as a factor in the product.

Exercise #1: Write each of the following in the form of an expanded product.

(a) x3 = (b) 45 = (c) ( 2x ) =

3

(d) ( x + 5 ) =

2

Exercise #2: Express each of the following with an equivalent expression involving exponents.

(a) z z z z z = (d) x x y y y = (b) 6 6 6 = (e) ( x + y )( x + y )( x + y ) = (c) 2a 2a 2a 2a =

Exercise #3: Consider the product shown below:

x 4 x3

(a) Write both parts of this product as extended products.

x4 =

x3 =

(b) Write the product x 4 x3 as an expanded product and in terms of an equivalent expression involving an exponent.

Exercise #4: Express each of the following products as a single variable raised to a power.

(a) x 2 x 7 (b) x 6 x 2 (c) a 2 a 3 a 4 (d) y 2 y 6 y10

Algebra 1, Unit #6 ­ Quadratic Algebra ­ L1 The Arlington Algebra Project, LaGrangeville, NY 12540

We also must be able to divide monomial expressions that have the same base. understanding how this process works is the following:

The key to

Any quantity divided by itself, except for zero, is equal to 1.

x5 . x3

(b) Rewrite the numerator of the quotient using (a).

Exercise #5: Consider the quotient

(a) Fill in the following: x5 = x 2 _______ .

(c) Rewrite the quotient as the product of two fractions, one of them being equal to 1.

(d) Simplify the quotient using the Multiplicative Identity Property of Real Numbers.

Exercise #6: Fill in the blanks in the box below: EXPONENT PROPERTIES

For any real numbers a and b, 1. x x = x

a b

_________

xa 2. b = x _________ x

Exercise #7: Write each product or quotient in its simplest form.

(a). (b) (c) (d) (e) (f) (g)

a4 a4 = x2 x7 =

(h)

10 y 8 = 6 y2

3 3 =

4 2

(i)

z3 = z2 b2 = b7 x2 y5 = x8 y 2

y2 y6 =

(j)

23 2 2 4 = y5 y 2 y =

(k)

(x )

3

2

=

(l)

(x )

2

3

x4

=

Algebra 1, Unit #6 ­ Quadratic Algebra ­ L1 The Arlington Algebra Project, LaGrangeville, NY 12540

Name: ____________________________________

Date: __________________

Exponents and Their Properties - Multiplying and Dividing Monomials Algebra 1 Homework Skill

Express the product with exponents. 1. a a a b b = 2. 3. 17.

x13 y 5 = x2 y9

( 2 x )( 2 x )( 2 x ) = ( 2 x )( 2 x ) y y =

18.

8 x5 y 3 = 4 x8 y10

y4 = y4

19.

Express the product in simplest form. b3 b = 4. 5. 6. 7. 8. 9. 10. 11.

Reasoning

Simplify. xc 20. = xd 21. 22. 23.

3

y 4 y9 =

c>d

x 2 x3 x 4 = n4 n =

y y =

z ( 2z ) ( 2z ) =

x 4a x 2a =

x3 x 6 x 4 = x5 x 2 y 2 a y 3a = ya

a a =

4 2

x3 x 7 =

24.

z4 z4 =

Express the quotient in simplest form. x5 13. = x4 14.

25.

x3 x 4

(x )

2

2

=

a10 = a4 x5 = x8

y6 = y12

26.

x4 y5 =

15.

Determine True or False for each. State the reason for your answer. x4 27. = 12 2 x 28.

16.

45 = 22 3 2

Algebra 1, Unit #6 ­ Quadratic Algebra ­ L1 The Arlington Algebra Project, LaGrangeville, NY 12540

Name: ____________________________________

Date: __________________

Exponents and Their Properties ­ Multiplying and Dividing Monomials Additional Practice Problems Skill

Find the product. 1. x5 x3 =

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Reasoning

Find each quotient. 43 20. = 4

21. x3 = x

y2 y = y y y =

4 2 6

Simplify. 4 x3 32. = 4x

33. t3 t 2 = t

aaaa = a6 a4 = t t =

3 7

22.

x5 = x2

y4 = y2 t2 = t2

34.

a · b3 = b2

23.

35.

( ab )

ab 2

2

=

r5 r3 =

x 4 x5 =

y3 y8 = t t =

24.

36.

x4 y 2 = x3 y 5 4x4 y2 = 2 xy 3

25.

z5 = z3

z9 = z5

37.

w w w w =

2 2

26.

38. 39.

xa xa =

xa = xb

x4 y7 z = x 2 yz 3 x4 y 2 = x4 y 2 xy 5 = x2 y 2 x2 y = x3 y 2

p5 p 3 p = x 6 x3 x = h8 h 3 = x4 x2 =

27.

t9 = t3

53 = 5

28.

40.

29.

y y=

2

p3 = p2

63 = 63

41.

xxx = m 23 m17 = b15 b5 =

30.

42.

31.

x12 = x10

43.

Algebra 1, Unit #6 ­ Quadratic Algebra ­ L1 The Arlington Algebra Project, LaGrangeville, NY 12540

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