WorkSHEET 3.2 Index laws Name: - Weebly
Transcript of WorkSHEET 3.2 Index laws Name: - Weebly
WorkSHEET 3.2 Index laws Name: ___________________________ Fluency 1 Write 3! in expanded factor form:
3! = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3
2 Write 9" in expanded factor form: 9" = 9 × 9 × 9 × 9
3 Given that 9 is the same as 3 × 3, Write your last answer in terms of the number 3.
9" = 9 × 9 × 9 × 9 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3
4 Take a look at your answer to question 1 and your answer to question 3. What can you say about 3! and 9"?
Clearly: 3! = eight 3’s multiplied together and 9" = eight 3’s multiplied together Without a calculator I don’t know what either answer is, but I do know they are the same value. Hence;
3! = 9"
5 Simplify each of the following (in index form). a 4 ´53 ´ 72 ´ 54 ´ 73
b 5 ´ e2 ´ f 2 ´ 3 ´ e3 ´ f 8 ´ 2 ´ e7 ´ f 5
Answers: a 4 ´ 53 ´ 72 ´ 54 ´ 73
= 4 ´ 53 ´ 54 ´ 72´ 73 = 4 ´ 53+4 ´ 72+3 = 4 ´ 57 ´ 75
c 5 ´ e2 ´ f2 ´ 3 ´ e3 ´ f8 ´ 2 ´ e7 ´ f5 = 5 ´ 3 ´ 2 ´ e2 ´ e3 ´ e7 ´ f2 ´ f8 ´ f5
= 30 ´ e2+3+7 ´ f2+8+5 = 30 e12 f15
WorkSHEET 3.2 Index laws
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6 Simplify each of the following. a (2h)5 b (a2b6)3 c (m3n2)4 ´ (m4n2)3
Answers: a (2h)5 = 21´5h1´5 = 25h5 = 32h5
b (a2b6)3 = a2´3b6´3 = a6b18
c (m3n2)4 ´ (m4n2)3 = m3´4n2´4 ´ m4´3n2´3
= m12n8 ´ m12n6 = m12+12 ´ n8+6 = m24n14
7 Simplify each of the following. (a)
(b)
Answers: (a)
(b)
8 Are the following statements true or false? (a) (–2)2 = –4 (b) 32 > 23 (c) 52 < 25
Answers: (a) False (b) True (c) True
9 Is the following statement true or false?
Answer: True
10 Apply first and second index laws to simplify the following expression.
Answer:
11 Simplify each of the following. (a) 2430 (b) 50 × 23 × 34
Answers: (a) 1 (b) 23 × 34
12 Simplify each of the following. (a) (b)
Answers: (a) 7 (b) −4
13 Simplify each of the following. (a)
(b)
Answers: (a) 5
(b)
52432 3210 babba ´´
zwwz
2
64
30425 ´
4 1260a b3 4103z w
138148
1829 qpqqp
=´
226432
373
6254
´´´´yxy
xxyyx11 7
47 6
2424x y x yx y
=
04 6+0 3(2 ) 5-
19 1920 3 (4 3 )´ ÷ ´0
0
6 5 73 4 6´ ´´ ´
54
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14 Raise each of the following to the given power. (a) (34)7 (b) (2530)11
Answers: (a) 328 (b) 255
15 Simplify;
4#
2#
13#
(5𝑎𝑏)#
2(5𝑎𝑏)#
Answers;
4# = 1
2# = 1
13# = 1
(5𝑎𝑏)# = 1
2(5𝑎𝑏)# = 2 × (5𝑎𝑏)# = 2 × 1 = 2
16 Simplify each of the following. (a)
(b)
Answers: (a) 66 (b) 334
6 Simplify each of the following.
(a)
(b)
Answers:
(a)
(b)
7 Simplify each of the following, giving your answers in index form. (a) (4j2)4 × (3j3m2)5 (b) 5a0 + 2a3i 2 × 3(ai 3)2
Answers:
(a) 44×35×j23m10 (b) 5 + 6a5i 8
2 3 5 0(6 ) (6 )´6 9
4 5
(3 )(3 )
552
93
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´
606
7604
43)5(
lklke
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143
3l
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8 Simplify each of the following, giving your answers in index form.
(a)
(b)
Answers: (a) 22x19y5
(b)
Simplify each of the following: (a) q10 ÷ q2 (b) d16 ÷ d 2 ´ d5
(c)
(d)
(e)
(f)
(a) q8 (b) d19
(c)
(d)
(e)
(f)
9 If z3 = 5, evaluate each of the following. (a) 7z3 – 4 (b) 2z9 (c) 4z6 + 3z0
Answers: (a) 31 (b) 250 (c) 103
10 At 1 pm, there were two bacteria in a Petri dish. If the number of bacteria doubled every 5 minutes, how many bacteria were in the dish at 2 pm. (use a calculator)
Answer: 8192
11 Expand 310 into factor form Expand 95 into factor form Expand 95 into factor form in Base 3 Show 95 as a base of 3
Answers: 310 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 95 = 9 × 9 × 9 × 9 × 9 95 = 9 × 9 × 9 × 9 × 9 = 32 × 32 × 32 × 32 × 32 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 95 = (32)5
= 310
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Without the aid of a calculator, simplify, leaving your answer in index form:
3$% × 25"
5& × 9"
=3$% × (5%)"
5& × (3%)"
=3$% × 5!
5& × 3!
= 3" × 5'
Without the aid of a calculator, simplify, leaving your answer in index form:
4$# × 7!
49& × 2'
=(2%)$# × 7!
(7%)& × 2'
=2%# × 7!
7( × 2'
= 2$' × 7%
If 𝑎 = 𝑥%, determine 𝑎": 𝑎" = (𝑥%)"
= 𝑥!
If 𝑎 = 2𝑥%, determine 3𝑎%: 3𝑎% = 3 × (2𝑥%)%
= 3 × 2% × 𝑥"
= 12𝑥"
If 𝑎 = 4𝑥%and 𝑏 = 2𝑥& determine %)!
*": 8𝑎&
𝑏" =2 × (4𝑥%)&
(2𝑥&)"
=2 × 4& × 𝑥(
2" × 𝑥$%
=2 × 64 × 𝑥(
16 × 𝑥$%
=8𝑥(
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By converting to a common ‘base’ , simplify the following:
Answer:
Simplify each of the following, giving the answer in index form. (a)
(b)
Answers:
(a) 3% × 3& × 2& × 2 × 3 = 3( × 2"
(b) 7%+,&-'+,$,"+ = 7&+,"
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