Unit 3 sec 3.4
fractional indices
12 November 2015
23:29
Meanings are given
for these indices, and you so that with these meanings. The index was at work
on negative in 0 indices.
Meanings can also be
given to fractional indices in such a way that the index laws work for these
indices.
Raising a number to the power half
is the same as taking it square root, raising the number to the power 3rd
is the same as taking its cue route and so on.
This rule, together with the index was that you have already
met, can be used to give a meaning of any fractional index.
Raising a number to the power is the
same as raising the nth root of the number of the power m.
The tool rules in the boxes above hold all the appropriate
numbers.
Powers like this do
have precise meanings, which you can learn about in detail in more advanced
mathematics modules. You can work out the value of to square root to as
accurately as you like by using as many decimal places of the decimal form of
square root of 2 as you like. The indices here, 1.414 and 1.414213, and so on
are rational, as they are determining decimal in power can be any real number.
All the index laws that have you have seen in this unit called for indices and
base numbers that are any real numbers, (except that the numbers must be
appropriate for the operations. For example, you could not divide by 0 or take
the square root of a negative number).
Powers and surds on
your calculator
the final activity of this section, you can practice using
your calculator from calculations involving powers, scientific notations and
surds.
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