Exponent Review #2
Day 15: February 14, 2014
Exponents and Radicals: You know that the appropriate radical will "undo" an exponent, and the right power
will "undo" a root. For example:
𝑥3 = 8
3
√𝑥 3 = 3√8
𝑥=2
√𝑥 = 2
2
(√𝑥) = (2)2
𝑥=4
OR
For the square (or "second") root, we can write it as the one-half power, like this:9-2009 All Rights Reserved
The cube (or "third") root is the one-third power:
The fourth root is the one-fourth power and so on.
RULE 5: Whenever you have a radical expression you can write the equivalent rational exponent
expression.
𝒏
𝟏
Specifically, √𝒂 = 𝒂𝒏
𝒏
𝒎
In General: √𝒂𝒎 = 𝒂 𝒏
OR
Notice: The root becomes the denominator and the exponent becomes the numerator.
Examples:
(1)
(2)
(3)
The Rules of Exponents are still valid for rational exponents!!!
Rule
Example
𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚𝑛
𝑎𝑚
= 𝑎𝑚−𝑛
𝑎𝑛
(𝑎𝑚 )𝑛 = 𝑎𝑚𝑛
Some Information in this worksheet was obtained from :
Stapel, Elizabeth. "Fractional (Rational) Exponents." Purplemath. Available from
http://www.purplemath.com/modules/exponent5.htm. Accessed 22 April 2009 and
http://regentsprep.org Oswego City School District Regents Exam Prep Center
Page 1
Exponent Review #2
Day 15: February 14, 2014
Rewrite and simplify the following expressions in rational exponent form.
1. √a
4.
7.
4
√𝑧 2
3.
5. √𝑥 3 𝑥 2 𝑥 7
6.
0
√𝑥 0
8.
6
√𝑦 0
3
10.
3
√x
2.
√𝑥 2
(𝑎4 𝑏 3 )
7
12
13. ( 3√𝑦)
√𝑥 6
5
√𝑥 3 𝑦 2 𝑦 9
3
√𝑥 2 ∙ √𝑥
√𝑎7
11. ( 3√𝑦)
√𝑥
9.
3
3
1
14. (𝑥 5 )5
4
12. ( √𝑥 )
4
1
15. (𝑥 10 )5
Solve for x. Round answers to 2 decimal places if necessary.
16. √𝑥 = 10
17. √𝑥 = 5
18. 𝑥 3 = 27
19. 𝑥 5 = 32
20. 𝑥 8 = 16
21. 𝑥 15 = 100
3
Some Information in this worksheet was obtained from :
Stapel, Elizabeth. "Fractional (Rational) Exponents." Purplemath. Available from
http://www.purplemath.com/modules/exponent5.htm. Accessed 22 April 2009 and
http://regentsprep.org Oswego City School District Regents Exam Prep Center
Page 2