We can also use exponential notation to represent a radical. To do so, we
use a rational exponent.
Recall that a rational number is a number that may be written as the ratio
of two integers.
So, a rational exponent may be a fraction, such as
, or an integer
Definition â€” Rational Exponent With Numerator 1
If a is a real number, then
Here, n is a positive integer.
If n is odd, then a1/n is a real number.
If n is even, then a1/n is a real number only when a
Using this definition, we write:
The way we interpret 2n depends upon
the value of n:
â€¢ n is a whole number
â€¢ n is zero
20 = 1
â€¢ n is a negative integer
â€¢ n is a fraction
Rewrite using a radical and evaluate: 1251/3
|Write the radical symbol.
|The index is 3, the denominator of the exponent
|The radicand is 125, the base of the exponential expression.
Find the prime factorization of 125.
125 = 5 Â· 5
Â· 5 = 53.
Since 53 = 125, the cube root of 125 is 5.