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4.3

Activity

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.

$<p>Horizontal axis, 0 to 2, by the fraction 1 over 3’s. Vertical axis, 0 to 4, by 0 point 2’s.</p>$
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.

Select one of the columns of the table that includes one of your estimates.
1. Write the power from the second row of the column you chose using radical notation.
2. What is the exact value of that number cubed?
3. Raise your decimal estimate from the table to the third power. What should it be? How close did you get?

Using exponent rules, we know is the same as because . But what about ?

Using exponent rules,

which means that

, so we could also write .

Here are more examples of exponents that are fractions and their equivalents: