Fractional Powers
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Transcript of Fractional Powers
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8/18/2019 Fractional Powers
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8/18/2019 Fractional Powers
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Fractional powers are useful when we need to calculate roots using a scientic calculator. Forexample to nd 7√ 38 we rewrite this as 381 / 7 which can be evaluated using a scientic calculator.You may need to check your calculator manual to nd the precise way of doing this, probably withthe buttons x y or x 1 /y .
Check that you are using your calculator correctly by conrming that381 / 7 = 1 .6814 (4 dp)
More generally we can write:
a m/n = n√ a m or equivalently n√ a m
Examples
82 / 3 = ( 3√ 8)2 = 2 2 = 4 , and 323 / 5 = ( 5√ 32)3 = 2 3 = 8
Alternatively,
82 / 3 = 3√ 82 = 3√ 64 = 4, and 323 / 5 = 5√ 323 = 5√ 32768 = 8
Exercises
3. Use a calculator to nd, correct to 4 decimal places, a) 5√ 96, b) 4√ 32.
4. Without using a calculator, evaluate a) 43 / 2
, b) 272 / 3
.5. Use the rule
a n
a m = a n − m with n = 0 to prove that a − m =
1a m
.
6. Each of the following expressions can be written as a n . Determine n in each case:
(a) 1
a 5 (b) √ a ×
1a 2
, (c) 1 (d) 1√ a .
Answers
1. (a) x 6 , (b) 1
x12 , (c)
1
t3 , (d) 4
3 , (e) 1
517 .
2. (a) 2− 3 = 123
= 18
, (b) 19
, (c) 16, (d) 32, (e) 64.
3. a) 2.4915, b) 2.3784. 4. a) 43 / 2 = 8 , b) 272 / 3 = 9 .
6. (a) −5 (b) −32 (c) 0 (d) −
12 .
www.mathcentre.ac.uk 2 c math centre 2009