learning intentions
to understand the meaning of an expression like (𝑏4)2(b4)2to be able to simplify expressions in which the index is zeroto be able to simplify expressions involving powers of powersto be able to expand expressions where a product is taken to a power, e.g. (𝑎𝑏)3
consider what the expanded form of (𝑎3)4(a3)4 would be:
(𝑎3)4===𝑎3×𝑎3×𝑎3×𝑎3𝑎×𝑎×𝑎 × 𝑎×𝑎×𝑎 × 𝑎×𝑎×𝑎× 𝑎×𝑎×𝑎𝑎12 (a3)4=a3×a3×a3×a3=a×a×a×a×a×a×a×a×a×a×a×a=a12
similarly:
(𝑏4)2===𝑏4×𝑏4𝑏×𝑏×𝑏×𝑏 × 𝑏×𝑏×𝑏×𝑏𝑏8(b4)2=b4×b4=b×b×b×b×b×b×b×b=b8
this leads us to an index law: (𝑎𝑚)𝑛=𝑎𝑚𝑛(am)n=amn.
work:
40+70 = 2
110 - 60 = 0
(2𝑥)0×(7𝑥𝑦)0 = 1
(5𝑎)0×(2𝑎𝑏)0 = 1
3𝑥0X4𝑥𝑦0 = 12x
12𝑦0×2𝑥0𝑦 = 24y
simplify
70 = 7
50×30 = 1
5𝑏0=5
12𝑥0𝑦2𝑧0 = 12y2
(3𝑥2)0 = 1
13(𝑚+3𝑛)0 = 13
2(𝑥0𝑦)2 = 2y2
4𝑥0(4𝑥)0 = 4
3(𝑎5𝑦2)0𝑎2 = 3a2
(23)4 = 212
(52)8 = 516
(64)9 = 636
(𝑑 3)3 = d9
(𝑘8)3 = k24
(𝑚5)10 = m50
(3𝑥5)2 = 9x10
(2𝑢4)3 = 8u12
(5𝑥5)4 = 54x20
(12𝑥5)3 = 123x15
(4𝑥4)2 = 16x8
(7𝑥2)2 = 49x4
(9𝑥7)10 = 910x70
(10𝑥2)5 = 105x10
(𝑥3)2×(𝑥5)3 = x21
(𝑦2)6×(𝑦3)2 = y18
(2𝑘4)2×(5𝑘5)3 = 500k23
(𝑚3)6×(5𝑚2)2 = 25m22
4(𝑥3)2×2(𝑥4)3 = 8x18
5( 𝑝2)6×(5𝑝2)3 = 54p18
(𝑦3)4
----- = 710
𝑦2
(𝑝7)2
------- = p8
(𝑝3)2
(2𝑝5)3
-------- = 2-13
22𝑝2
(3𝑥2)10
---------- = 310x14
(𝑥3)2
8ℎ20
------- = 8h5
(ℎ3)5
(𝑞2)10
-------- = q2
(𝑞3)6
YOU ARE READING
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