**Rational exponents.**
Let be a positive integer,
and let be a positive real number.
Then we can find a unique value
so that .
We call such value the *-th root* of ,
and write ``
.''
Furthermore,
for any rational number
we can define the *rational exponents*
by

and

**Irrational exponents.**
Let be an irrational number.
Then, for a rational number
arbitrarily close to
we can find a unique value so that
the rational exponent
becomes arbitrarily close to .
We call such value the *irrational exponent* .

**Compound interest.**
Suppose that represents the principal, and that is an interest
rate.
The amount after interest period is expressed by

**The number .**
We can find a unique value
so that

(1) |

Department of Mathematics