Question 672074
 Definition:

    If the power or the exponent raised on a number is in the form {{{p/q}}}, where {{{q <>0}}}, then the number is said to have {{{rational}}}{{{ exponent}}}. 

For example: {{{8^(1/3)}}}, means to take the 3-th root of {{{8}}}


Exponents can accept values from the multitude of the real numbers. They can be both rational or irational. 

Irrational exponents: 

Let {{{x}}} be an irrational number. Then, for a rational number  {{{m/n}}} arbitrarily close 
to {{{x}}} we can find a unique value {{{ b > 0}}} so that the rational exponent  {{{ a^(m/n)}}} becomes arbitrarily close to {{{b}}}. We call such value {{{b}}} the irrational exponent {{{a^x}}}.