FreeAlgebra Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Solving Equations with a Fractional Exponent

An expression that contains a fractional exponent can be written using a radical. Fractional exponents are often referred to as rational exponents.

Definition â€” Rational Exponent

If a is a real number, and m and n are natural numbers, then:

Here we assume that if n is even then a 0.

Here are two examples:

Notice that in am/n the number in the denominator of the fraction, n, becomes the index in the radical,

Example

Solve for x: (2x - 6)2/3 - 7 = -3

 Solution (2x - 6)2/3 - 7 = -3 First, rewrite (2x - 6)2/3 as a radical. = -3 Step 1 Isolate a radical term. Add 7 to both sides. Step 2 Apply the Principle of Powers. = 4 Cube each side of the equation. = (4)3 Step 3 Solve the resulting equation. Simplify. Write the left side as a product. Simplify. (2x - 6)2 (2x - 6)(2x - 6) 4x2 - 24x + 36 = 64 = 64 = 64 Write in standard form. Divide both sides by 4. Factor. Use the Zero Product Property. Solve for x. Step 4 Check the solution. 4x2 - 24x - 28x2 - 6x - 7 (x - 7)(x + 1) x - 7 = 0 or x + 1 x = 7 or x = 0= 0 = 0 = 0 = -1

We leave the check for you (both solutions check).

So, the solutions are x = 7 and x = -1.