IM Alg2.3.4 Lesson: Positive Rational Exponents
Find the value of each expression mentally.
Use exponent rules to explain why these expressions are equal to each other:
Write using radicals.
Write using radicals. Show your reasoning using exponent rules.
Complete the table as much as you can without using a calculator. (You should be able to fill in three spaces.)
Plot the points that you filled in. Connect the points as smoothly as you can.
Use this graph of to estimate the value of the other powers in the table, and write your estimates in the table.
Let’s investigate : Write using radical notation.
What is ?
Raise your estimate from the table of to the third power. What should it be?
How close did you get?
Let’s investigate : Write using radical notation.
What is the value of ?
Raise your estimate from the table of to the third power. What should it be? How close did you get?
Answer these questions using the fact that Explain why is very close to . Is it larger or smaller than ?
Is it possible to write exactly with a finite decimal expansion? Explain how you know.