The two in the
expression is called
the *base*,
and the 3 is called
the *exponent*
(or power).

Do you
actually
need to
use math
exponents?

The answer
is
no
. People
didn't
begin to
use
exponents
until a
few
hundred
years
ago.

It is OK
to
multiply
out the
numbers
and use
the
result
. That is
what
people did
until
exponents
were
invented.

In the
example
shown
above,
.
You can
just
use
the
8
*rather
than*
2^{3}
if you
wish.

So what is
the point
of using
math
exponents?

The
primary
reason
for using
exponents is
because
exponents
are shorthand
notations which
allow us
to deal with
extremely large
and extremely
small
numbers
more
easily
than using the
standard form
of a number. In
addition,
fractional
exponents
simplify
calculations
involving
radicals.

Exponents make
the following
common
applications
possible:

Why use
exponents?
Exponents
make many
calculations
fast and
easy .
But again, you
can use the
standard form
of a number if
you wish - and
forget all
about
exponents.

For
example:

Multiply
the following
two numbers
together:

5^{10}
*
5^{6}

Finding the
result
without
using
exponents
is time
consuming and
tedious:

5^{10}

=

5
*
5
*
5
*
5
*
5
*
5
*
5
*
5
*
5
*
5

=

9,765,625

5^{6}

=

5
*
5
*
5
*
5
*
5
*
5

=

15,625

9,765,625
*
15,625
=
152,587,890,625
(final
answer)

Note: if you
have tried to
multiply the
two numbers
shown above,
you know that
most
calculators are
not accurate
when computing
numbers beyond
8 or 10 digits
(the numbers
are
automatically
rounded by the
calculator).
However, you
can
download an
excellent
precision
calculator
which can
handle
thousands of
digits for
free at
http://download.cnet.com/windows/karenware-com/3260-20_4-10025295-1.html

Finding the
result
using
exponents
is fast and
easy:

5^{10}
*
5^{6}

=

5^{10+6}

=

5^{16}

(final
answer)

Math
Exponents:
impact
your
day-to-day
finances

Although
most
people may
not stop
to think
about it,
exponents
impact
most
routine
financial
transactions,
either
directly
or
indirectly.
Banks,
credit
unions,
the
government,
car
dealerships,
and other
businesses
use
exponents
to
calculate
interest
and
penalties.

For
example:

When you
deposit
money in a
bank, the
bank will
use
exponents
to
calculate
how much
interest
you
account
has
earned
. If the
bank will
pay you
compound
monthly
interest
on your
deposit,
the
formula
used
is:

Total
$
*in Your
Account
=* (
Original
Deposit)(
1+r
) ^{(
m
)}

**r**
= monthly
interest
rate
entered as
a decimal
(eg - 1%
interest
per month
would be
entered as
0.01);
the
exponent,
**m**
*=
number of
months
money is
left in
the
account*

If you
deposit
$100 in an
account
which pays
1%
compounded
interest
per month,
and leave
your money
in the
account
for 14
months,
your
balance
can be
calculated
as:

Total
$
*in Your
Account
=* (
$100
Deposit)(
1+0.01
) ^{(
14
)}

=
$114.95