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5 2 Practice

The document contains additional practice problems for Algebra 2 focused on properties of exponents and radicals. It includes exercises for rewriting expressions, simplifying radicals, and performing operations with radical expressions. The document is structured with numbered problems and provides a variety of mathematical scenarios for practice.

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Zachary Nguyen
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28 views1 page

5 2 Practice

The document contains additional practice problems for Algebra 2 focused on properties of exponents and radicals. It includes exercises for rewriting expressions, simplifying radicals, and performing operations with radical expressions. The document is structured with numbered problems and provides a variety of mathematical scenarios for practice.

Uploaded by

Zachary Nguyen
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Name ALGEBRA 2

SavvasRealize.com

5-2 Additional Practice


Properties of Exponents and Radicals

Rewrite each expression using the properties of exponents.


_
​  12 ​ _
3
​  ​
( ​64​​  ​ 6​)
_1 _1 2 _1 6
4 2. ​​3m​​  4 ​​​​​(​mn​​  3 )​​​  ​​
​  1 ​ 2 3. ​​2a​​  ​  2 ​​​​​​(​5a​​  ​  2 ​ ​b​​  ​  4 ​)​​​  ​​ 4. ​​​(​x​​  ​  3 ​​ · ​x​​  ​  9 ​​)​​​  ​​ ÷ ​​x​​  ​  3 ​​​
___ _
​  1 ​ _ _1 _1 _1
1. ​​​ ​  _5 ​ ​​​  ​​

How can you rewrite each _____


expression? ________
________ ________
5. ​​ √
3
125​x​​  9​​y​​  7​ ​​ √ 625a
4 5 3
​  ​a​​  ​​b​​  ​​
6. ​​ _____  ​​ 7. ​​ √
5
288​x​​  3​​y​​  7​ ​​ √
8. ​​ ________
3
4 5
​  297​m2​​  ​​n​​  ​​ ​​
3​m​​  ​n

What is the reduced radical form of each expression?


___ ___ _____ _____

√ 36x
___ 2 ____
​​(​√ ​4​​  5​ ​)​​​​(​√ ​5​​  5​ ​)​​
3
9. (​​​ ​√ 32 ​)​​​  ​​
4
10.
3 3
11. √​​ ​a​​  3​​b​​  5​ ​​ · 5​​√4ab ​​ ​  24​x​​  ​​ ​​
12. ​​ _____
3

How can you rewrite each expression in a simpler form?


3
_____ 3
__ 3
_____ ___ ____ ____
13. ​​ √ 3000 ​​ + ​​ √ 3 ​​ − ​​ √ 1029 ​​ ​​ 45 ​​ − ​​√180 ​​ − √
14. √ ​​ 720 ​​

Multiply.
__ __ ___ __ __
15. (x − √
​​ 8 ​​)(x + √
​​ 8 ​​) ​​ 12 ​​(√
16. √ ​​ 3 ​​ + ​​√6 ​​)

What is the reduced radical form of each expression?


__
√
​​  3 − ​ 7 ​
17. ______ __ ​​  −5x√__ ​​
​18. ______
3−√ ​ 5 ​ 3 − ​ x ​

___ __
​​ 50 ​​ + ​​√k ​​ can be written as a
19. Discuss the possible values of k such that √
single term.
___
20. Write ​​ √ ​  16
__ ​ ​​in
two different ways, one where the number is simplified and
7
another where the denominator is rationalized.
__ __
21. The length of a rectangle is (3 + ​​√7 ​​)m and its width is (1 + 2​​√7 ​​)n. What is the
area of the rectangle?

enVision® Florida Algebra 2 • Teaching Resources

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