A rational exponent is an exponent in the form of a fraction. Any expression that contains the square root of a number is a radical expression. Both have real world applications.

## Rational Exponent Examples

In a rational exponent, the denominator, or bottom number, is the root, while the numerator, or top number, is the new exponent. In the following examples, the carrot symbol indicates that the right half is the exponent of the left. For example:

x ^ (1/2) = √x (square root of X)

x ^ (1/3) = 3√x (cube root of X)

A radical expression is any expression or equation that contains a square root. The square root symbol indicates the number inside is a radical. The number inside the square root is called the radicand. Variable numbers can also be radical expressions. For example:

√x+y

√16

12+√x

√3*x²

## Real World Examples of Rational Exponents

The financial industry uses rational exponents to compute interest, depreciation and other kinds of regular calculations.

For example, to calculate the inflation of a home that increases in value from p1 to p2 over a period of n years, the annual rate of inflation (expressed as a decimal) is i = (p2/p1)^(1/n) -1.

To calculate compound interest, the formula is F = P (1+i)^n , where F is the future value and P is the present value, i is the interest rate and n is the number of years. If you wanted to calculate the compound interest on \$1,000 for 18 months at 5 percent, the formula would be F = 1000 (1+.05)^(3/2).

## Real World Examples of Radical Expressions

Radical expressions are common geometry and trigonometry, particularly in triangles.

The ratio of the sides of a 30°- 60°- 90° right triangle is 1:2:√3, and the ratio of the sides of a 45°- 45°- 90° right triangle is 1:1:√2. Triangles are common in the building trades, especially in carpentry and masonry.

One of the simplest formulas in electrical engineering is for voltage, V = √PR, where P is the power in watts and R is the resistance in ohms.