IM Alg2.3.5 Lesson: Negative Rational Exponents

Evaluate mentally.
[math]9^2[/math]
[math]9^{-2}[/math][br]
[math]9^{\frac{1}{2}}[/math]
[math]9^{-\frac{1}{2}}[/math]
Complete the table as much as you can without using a calculator. (You should be able to fill in three spaces.)
Plot these powers of 2 in the coordinate plane. ​​​​​​Connect the points as smoothly as you can.
Use your graph of [math]y=2^x[/math] to estimate the value of the other powers in the table, and write your estimates in the table.[br]
[size=150]Let’s investigate [math]2^{\text{-}\frac{1}{3}}[/math].[/size][br][br]Write [math]2^{\text{-}\frac{1}{3}}[/math] using radical notation.
What is the value of [math](2^{\text{-}\frac{1}{3}})^3[/math]?[br]
Raise your estimate of [math]2^{\text{-}\frac{1}{3}}[/math] to the third power. What should it be? [br]
How close did you get?
[size=150]Let’s investigate [math]2^{\text{-}\frac{2}{3}}[/math].[br][/size][br]Write [math]2^{\text{-}\frac{2}{3}}[/math] using radical notation.
What is [math](2^{\text{-}\frac{2}{3}})^3[/math]?[br]
Raise your estimate of [math]2^{-\frac{2}{3}}[/math] to the third power. What should it be? [br]
How close did you get?
For each set of 3 numbers, cross out the expression that is not equal to the other two expressions.
For each expression, write an equivalent expression using radicals.
[math]17^{\frac{3}{2}}[/math]
[math]31^{\frac{3}{2}}[/math]
For each expression, write an equivalent expression using only exponents.
[math](\sqrt{3})^4[/math]
[math]\frac{1}{(\sqrt[3]{5})^6}[/math]
Write two different expressions that involve only roots and powers of 2 which are equivalent to [math]\frac{4^{\frac{2}{3}}}{8^{\frac{1}{4}}}[/math].
Match expressions into groups according to whether they are equal. Be prepared to explain your reasoning.
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– GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

Information: IM Alg2.3.5 Lesson: Negative Rational Exponents