Transcript w) Indices and Exponential Graphs - Student - school

Indices and
Exponential Graphs
Learning Outcomes
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I can add, subtract, multiply and divide terms containing indices
I can calculate with negative indices
I can calculate with fractional indices and represent as roots
I can write very large and very small numbers in standard form
I can add, subtract, multiply and divide in standard form
I can solve equations with indices
I can recognise and draw graphs of exponential functions, y=aⁿ,
y=a-ⁿ
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I can use exponential graphs in real life situations
Indices
Indices
am x an = am+n
(add indices when multiplying)
2) x5 x x-2 =
1) x2 x x8 =
am ÷ an = am-n
(subtract indices when dividing)
2) 30x5 ÷ 10x-2 =
1) x6 ÷ x4 =
(am)n
2) (3x3)2 =
1) (x2)5 =
a0 = 1
1) x0 =
(when we have a number in index form
raised to a power we multiply the indices)
3) (4x2y3)3 =
(any number t the power of 0 is equal to 1)
2) p0 =
Indices
Applying the Laws
of Indices
Find:
a) 4½
b) 8 1/3
c) 32 1/5
d) 43/2
e) 8 5/3
f) 32 4/5
g) 16 3/4
You need to know:
N
N2
N3
N4
N5
1
1
1
1
1
2
4
8
16
32
3
9
27
87
243
4
16
64
5
25
125
6
36
216
Indices
Negative Indices
Rule: a-n = 1
an
To evaluate a number in index form with a negative index, You simply turn the
term upside down and remove the minus sign
a) 25 -3/2
b) 0.008 -2/3
Indices
Additional Notes
Indices and
Exponential Graphs
Learning Outcomes:
At the end of the topic I will be able to
Can
Do
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I can add, subtract, multiply and divide terms containing
indices
I can calculate with negative indices
I can calculate with fractional indices and represent as roots
I can write very large and very small numbers in standard form
I can add, subtract, multiply and divide in standard form
I can solve equations with indices
I can recognise and draw graphs of exponential functions,
y=aⁿ, y=a-ⁿ
I can use exponential graphs in real life situations
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Revise
Further
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