Algebra Tutorials!    
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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
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
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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 · w(-3/2) = w1/6


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.


w1/3 · 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.



Example 2

Simplify and write using only positive exponents:


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 




We could use radical notation to write

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