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 ´5 3 ´ 7 2 ´ 5 4 ´ 7 3 b 5 ´ e 2 ´ f 2 ´ 3 ´ e 3 ´ f 8 ´ 2 ´ e 7 ´ f 5 Answers: a 4 ´ 5 3 ´ 7 2 ´ 5 4 ´ 7 3 = 4 ´ 5 3 ´ 5 4 ´ 7 2 ´ 7 3 = 4 ´ 5 3+4 ´ 7 2+3 = 4 ´ 5 7 ´ 7 5 c 5 ´ e 2 ´ f 2 ´ 3 ´ e 3 ´ f 8 ´ 2 ´ e 7 ´ f 5 = 5 ´ 3 ´ 2 ´ e 2 ´ e 3 ´ e 7 ´ f 2 ´ f 8 ´ f 5 = 30 ´ e 2+3+7 ´ f 2+8+5 = 30 e 12 f 15
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WorkSHEET 3.2 Index laws Name: ___________________________ Fluency 1 Write 3! in expanded factor form:
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
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