How does a rational exponent look like?

A rational exponent is written as x a b , x^{ \frac{a}{b}}, xba​, with base x x x and exponent a b \frac{a}{b} ba​. Note that the exponent is applied first, before the radical, and also that if the base is negative, taking roots is no longer simple, and requires Complex Number Exponentiation.

How do you solve rational equations?

  1. Solution:
  2. Step 1: Factor all denominators and determine the LCD.
  3. Step 2: Identify the restrictions. In this case, they are x≠−2 x ≠ − 2 and x≠−3 x ≠ − 3 .
  4. Step 3: Multiply both sides of the equation by the LCD.
  5. Step 4: Solve the resulting equation.
  6. Step 5: Check for extraneous solutions.

What is a rational exponent in math?

Rational exponents (fractional exponents) are exponents that are fractions or rational expressions. A rational exponent can be converted to its equivalent radical form. Exponent laws can be applied to rational exponents in the same way they work for any other types of exponents.

What is an example of a rational exponents?

A rational exponent is an exponent that is a fraction. For example, √4 can be written as 412 4 1 2 . Can’t imagine raising a number to a rational exponent? They may be hard to get used to, but rational exponents can actually help simplify some problems.

How do you simplify powers?

This leads to another rule for exponents—the Power Rule for Exponents. To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, (23)5 = 215. For any positive number x and integers a and b: (xa)b= xa· b.

What are examples of rational exponents?

A rational exponent is an exponent in the form of a fraction. When relating rational exponents to radicals, the bottom of the rational exponent is the root, while the top of the rational exponent is the new exponent on the radical. Example: x^(2/3) {x to the two-thirds power}. = √x {the cube root of x squared}. Example #2:

What are the rules for rational exponents?

Some basic rational exponent rules apply for standard operations. When multiplying exponents, we add them. When dividing exponents, we subtract them. When raising an exponent to an exponent, we multiply them. If the problem has root symbols, we change them into rational exponents first.

How do you simplify complex rational equations?

In order to simplify complex rational expressions, it is important to be able to find the lowest common denominator. Complex rational expressions are fractions that are divided by fractions. When you have found the lowest common denominator, then, you should multiply both fractions by the common denominator.

How do you simplify an exponential expression?

Simplifying Exponential Expressions. Recall that to simplify an expression means to rewrite it by combing terms or exponents; in other words, to write the expression more simply with fewer terms. The rules for exponents may be combined to simplify expressions. Simplify each expression and write the answer with positive exponents only.