Unit 6, Lesson 9
Unit Fractional Exponents
Algebra 1
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For each equality, find the missing exponent that will make the statement true. Be prepared to explain your reasoning.
Take turns with your partner to complete the table so that each row of the table has an equivalent value in all three columns.
| exponents | roots | values |
|---|---|---|
| 8 | ||
| 2 | ||
| 10 | ||
| 5 |
We can use exponent rules and the meaning of roots to rewrite certain roots as exponents and certain exponents as roots!
From an exponent rule, we know that because .
Based on the meaning of roots, we know that , as well.
Because both expressions are equal to , this means that . We’re using only positive base values in this unit, so the parts without the "" exponent must be equivalent. That means that .
For example, , which is true because .