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:

# Equations Involving Rational Exponents

Equations involving rational exponents can be solved by combining the methods that you just learned for eliminating radicals and integral exponents. For equations involving rational exponents, always eliminate the root first and the power second.

Example 1

Eliminating the root, then the power

Solve each equation.

a) x2/3 =4

b) (w - 1)-2/5 = 4

Solution

a) Because the exponent 2/3 indicates a cube root, raise each side to the power 3:

 x2/3 = 4 Original equation (x2/3)3 = 43 Cube each side. x2 = 64 Multiply the exponents: x = 8 or x = -8 Even-root property

All of the equations are equivalent. Check 8 and -8 in the original equation. The solution set is {-8, 8}.

 = 4 Original equation [(w - 1)-2/5]-5 = 4-5 Raise each side to the power -5 to eliminate the negative exponent. (w - 1)2 Multiply the exponents: w - 1 Even-root property w - 1 or w - 1 w or w

Check the values in the original equation.The solution set is .

An equation with a rational exponent might not have a real solution because all even powers of real numbers are nonnegative.

Note how we eliminate the root first by raising each side to an integer power, and then apply the even-root property to get two solutions in Example 1(a). A common mistake is to raise each side to the 3/2 power and get x = 43/2 = 8. If you do not use the even-root property you can easily miss the solution -8.