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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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