Algebra Tutorials! Monday 19th of March

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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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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 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