1. Manipulating Indices
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2. A Summary on the Rules of Indices
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3. A Summary on the Rules of Indices1. 2.
Special Results
a 0 = 1
a 1 = a
1n = 1
0n = 0 (unless n = 0) 3. 4. 5. 6. 7. 8.
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4. It is often required to evaluate expressions involving indices without using a calculator
Typical intermediate questions:
Higher tier questions:
Higher tier, A* questions:
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5. Evaluating such expressions requires:
It is often required to evaluate expressions involving indices without using a calculator
Evaluating such expressions requires:
Knowing the rules of indices
Using them effectively
Recognising certain “patterns” or “themes”
Recognising small powers of 2,3,4, … , 10
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6. Examples on manipulating & evaluating indices
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7. Examples on manipulating & evaluating indices
The next 2 examples require to change the base of the power, as well as applying the rules of indices competently.
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8. Exam Question
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9. If x = 2m and y = 2n , express the following in terms of x and/or y only:
1. 2m + n m
3. 2n – 2 1.
2m + n = 2m
x 2n
= x x y
= xy
[ ]3 2.
23m =
23 x m
= 2m
= x 3 1 4 y 4 3.
2n – 2 = 2n
x 2-2
= 2n x
= y x 1 4 = y 4 = 2n
÷ 22
= 2n ÷ 4
= y ÷ 4 =
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