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
= 35 - 3 - (34)1/2
= 35 - 3 - 32
= 243 - 3 - 9
= 231
7. Answer :
= (-1/4)-2 - 3 x 82/3 x 40 + (9/16)-1/2
= (-4)2 - 3 x (23)2/3 x 1 + (16/9)1/2
= 16 - 3 x 22 x 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)2 + (-3)2 + (-4)2
= 22 + 32 + 42
= 4 + 9 + 16
= 29
10. Answer :
= (-1/3)-4
= (-3)4
= 34
= 81
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