SIMPLIFY USING LAWS OF EXPONENTS WORKSHEET

Simplify each of the following :

Question 1 :

(-7)2 x (-3)3

Question 2 :

(-2)5 x (-1)83

Question 3 :

(-4)5 ÷ (-4)8

Question 4 :

(-3)4 x (5/3)4

Question 5 :

 (3)-7 ÷ 310) x 3-5

Question 6 :

95/2 - 3 x 50 - (-1/81)-1/2

Question 7 :

(-1/4)-2 - 3 x 82/3 x 40 + (9/16)-1/2

Question 8 :

[(-2/3)-2]2

Question 9 :

(-1/2)-2 (-1/3)-2 (-1/4)-2

Question 10 :

(-1/3)-4

General Fact : 

When we take even exponent for a negative number, it will become positive and when we take odd exponent to a negative number it will still be negative.

1. Answer :

= (-7)2 x (-3)3

= 72 x (-33)

= 49 x (-27)

= -1323

2. Answer :

= (-2)5 x (-1)83

-25 x (-1)

= -32 x (-1)

= 32

3. Answer :

= (-4)5 ÷ (-4)8

= -45 ÷ 48

= -45-8

= -4-3

= -1/43

= -1/64

4. Answer :

= (-3)4 x (5/3)4

= 34 x (54/34)

= (34 x 54)/34

= 34-4 x 54

= 30 x 54

= 1 x 625

= 625

5. Answer :

= (3-7 ÷ 310) x 3-5

= 3-7-10 x 3-5

= 3-17 x 3-5

= 3-17-5

= 3-22

= 1/322

6. Answer :

= 95/2 - 3 x 50 - (1/81)-1/2

= (32)5/2 - 3 x 1 - (81)1/2

= 3- 3 - (34)1/2

= 3- 3 - 32

= 243 - 3 - 9

= 231

7. Answer :

= (-1/4)-2 - 3 x 82/3 x 40 + (9/16)-1/2

= (-4)- 3 x (23)2/3 x 1 + (16/9)1/2

= 16 - 3 x 2x 1 + [(4/3)2]1/2

= 16 - 3 x 4 x 1 + 4/3

= 16 - 12 + 4/3

= 4 + 4/3

= (12 + 4)/3

= 16/3

8. Answer :

= [(-2/3)-2]2

= [(-3/2)2]2

= (-3/2)4

= (3/2)4

= 34/24

= 81/16

9. Answer :

= (-1/2)-2 (-1/3)-2 (-1/4)-2

= (-2)(-3)(-4)2

= 2342

= 4 + 9 + 16

= 29

10. Answer :

= (-1/3)-4

= (-3)4

= 34

= 81

Video Lessons

Introduction to Exponents

Laws of Exponents - 1

Laws of Exponents - 2

Laws of Exponents - 3

Laws of Exponents - 4

Important Stuff

Problem - 1

Problem - 2

Problem - 3

Problem - 4

Problem - 5

Problem - 6

Problem - 7

Problem - 8

Problem - 9

Problem - 10

Problem - 11

Problem - 12

Problem - 13

Problem - 14

Problem - 15

Problem - 16

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