Algebra Tutorials! Monday 20th of January   Home Scientific Notation Notation and Symbols Linear Equations and Inequalities in One Variable Graphing Equations in Three Variables What the Standard Form of a Quadratic can tell you about the graph Simplifying Radical Expressions Containing One Term Adding and Subtracting Fractions Multiplying Radical Expressions Adding and Subtracting Fractions Multiplying and Dividing With Square Roots Graphing Linear Inequalities Absolute Value Function Real Numbers and the Real Line Monomial Factors Raising an Exponential Expression to a Power Rational Exponents Multiplying Two Fractions Whose Numerators Are Both 1 Multiplying Rational Expressions Building Up the Denominator Adding and Subtracting Decimals Solving Quadratic Equations Scientific Notation Like Radical Terms Graphing Parabolas Subtracting Reverses Solving Linear Equations Dividing Rational Expressions Complex Numbers Solving Linear Inequalities Working with Fractions Graphing Linear Equations Simplifying Expressions That Contain Negative Exponents Rationalizing the Denominator Decimals Estimating Sums and Differences of Mixed Numbers Algebraic Fractions Simplifying Rational Expressions Linear Equations Dividing Complex Numbers Simplifying Square Roots That Contain Variables Simplifying Radicals Involving Variables Compound Inequalities Factoring Special Quadratic Polynomials Simplifying Complex Fractions Rules for Exponents Finding Logarithms Multiplying Polynomials Using Coordinates to Find Slope Variables and Expressions Dividing Radicals Using Proportions and Cross Solving Equations with Radicals and Exponents Natural Logs The Addition Method Equations
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:

# Rational Exponents

Before we rewrite an exponential expression as a radical, we must make sure that the rational exponent is reduced to lowest terms.

Example 1

Simplify and write using only positive exponents: w1/3 Â· w(-3/2) = w1/6

Solution

 Each factor has the same base, w. Therefore, add the exponents and keep w as the base. Write each fraction with the LCD, 6. Add the exponents. Simplify. w1/3 Â· w(-3/2) = w1/6 = w1/3 + (-3/2) + 1/6 = w2/6 - 9/6 + 1/6 = w -6/6 = w -1 Use to write the expression using a positive exponent. Therefore, Example 2

Simplify and write using only positive exponents: Solution

There is more than one way to start simplifying.

 We begin with the Power of a Quotient Property. Use the Power of a Product Property to raise each factor to the power -3. Use the Power of a Power Property. Use the following to write the coefficients with positive exponents:  Evaluate the coefficients and simplify  So, Note:

We could use radical notation to write 