2 Algebraic Expressions

2 Algebraic Expressions 2.1

Laws of Exponents

Write each expression as a single power with a positive exponent.

Laws of Exponents (a ≠ 0) 0

a xa =a

1

a ÷a =a

a =1

1. 2 8 x 2 5 = 2

8+5

= 213

same base

2. 2 8 ÷ 2 5 = 2

=

same base



40

-8

= 2 =



-p

Keep the base and subtract the exponents.

23 8x5

Keep the base and multiply the exponents.

1 28

1 p a

n

m+n

m

n

m–n

m n

mxn

(a ) = a

(m and n are natural numbers.)

(p is an integer.)

A 65 x 62 = 6

+

B 65 ÷ 62 = 6

–

C (65)2 = 6

Write each expression as a single power with a positive exponent.

24

a =a a =

8–5

3. (2 8)5 = 2

4. 2

Keep the base and add the exponents.

m

x

= 6 = 6

= 6

1 D 6-5 = 6

A 108 ÷ 105 =



B 43 x 42 =



C 5-8 =

D 37 x 33 =



E 56 ÷ 5 =



F (63)3

G 4-2 =



H (72)4 =



I (8-3)2 =

J 83 x 84 =



K (6-1)2 =



Excerpt from L 34 ÷ 3 =

=

Complete MathSmart Grade 9

M 52 ÷ 50 x 53 =



N 93 x 9 ÷ 92 =#popularbookcompany

O (72)3 x 72 =



P (82)3 ÷ (82)2 =

Q (3-2)3 x 35 =



R (10-2)4 x (103)2 =

Complete MathSmart (Grade 9)

Popular Book Company (Canada) Ltd.

ISBN: 978-1-77149-220-1

www.popularbook.ca

Write each expression as a base of 2 or 3 with a positive exponent. 3

S 8 =



95

4

T 81 =

-5

U 9 =



V 64 =

W 2432 =



X 47 =

Y 10243 =



Z 27-4 =

Think: 9 = 32 Replace 9 by 32.

= (32)5 10 = 3

-2

Keep the base and multiply the exponents. m n

mxn

(a ) = a

Write each expression as a single power. Then evaluate each power. a

43 ÷ 22 20 x (23)3

d

(52)2 5 x 253 -3

b

52 x 54 ÷ 53 50 + 22

e

3-6 9 ÷3 x 3 0 2 +2 8

2

c

(72)3 x 74 ÷ 7 (49)3 ÷ 70

f

5123 x 2-9 ÷ 28 92 ÷ 9 – 50

Excerpt from

Complete MathSmart Grade 9 #popularbookcompany

g

644 ÷ (27 x 26) = 52 – 32

i

k

(613 ÷ 6) = 52 – 50 + 23



h

216-4 x

(56)2 ÷ (53 x 52) = 53 ÷ 125



j

243 x 36 = 54 ÷ 52 + 26 ÷ 25

83 x (43 ÷ 27) 64 ÷ 23 ÷ 2



l

54 – 33 = 96 ÷ 39 x 81

ISBN: 978-1-77149-220-1

=

Popular Book Company (Canada) Ltd.

Complete MathSmart (Grade 9)

www.popularbook.ca

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