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I. Model Problems.
II. Practice
III. Challenge Problems
VI. Answer Key
Web Resources
Video and Extra practice on
How to Simplify Fractional Exponents
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I. Model Problems
To simplify fractional exponents, rewrite the expression as a radical
raised to a power. The denominator of the fractional exponent is the
root and the numerator is the power.
In other words: xm/n =
n
xm =
 
n
m
x
Example 1 Write 272/3 as a radical and simplify.
272/3 =
 
3
Rewrite as a radical.
2
27
= 32
=9
The answer is 9.
Simplify.
Simplify.
Sometimes you need to write a radical expression using a fractional
exponent.
Example 2 Write
4
4
y 6 using a fractional exponent.
y 6 = y6/4
= y3/2
Rewrite as a fractional exponent.
Simplify.
The answer is y3/2.
Sometimes there will be many variables in the radicand. Simplify each
variable one at a time, then multiply.
Example 3 Simplify 3 8x5 y 6 z11 .
3
8x5 y 6 z11 = 3 8  3 x5  3 y 6  3 z11
Rewrite the expression.
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= 2  x 3 x2  y2  z3 3 z 2
Simplify.
= 2xy 2 z 3  3 x 2 z 2
Simplify.
The answer is 2xy 2 z 3  3 x 2 z 2 .
Practice Problems are on next page
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II. Practice
Evaluate.
1. 251/2
2. 10002/3
3. 1213/2
 4
4.  
 9
5. 16–5/2
6. (–216)–1/3
 1 
7. 
 125 
9. 323/5
1/3
1/ 2
8. 49–1/2
10. 0.041/2
Simplify.
a7
12.
5
z11
13. 4 16c5 d 8
14.
3
27a3b5
11.
3
15.
5
243x11 y8 z 20
16. 3 8x5 y 6
17.
6
a 4 b8 c12
18.
19.
3
m13 n8 p9
20. 5 64r 13s15t12
3
40d 5e6 f 4
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III. Challenge Problems
21. What is the value of 641/12•643/12?
497/ 2
22. What is the value of 3/ 2 ?
49
23. Correct the Error
There is an error in the student work shown below:
3
3
24a 3 b 4 c 7 =
3
3
24 3 a 3 b 4 c 7 =
3
= 2ac 2 3bc
What is the error? Explain how to solve the problem.
_________________________________________________________
_________________________________________________________
24. Circle the expression that is greater:
(a) (–4)2/3 OR (–4)3
(b) 41/2 OR 4–1/2
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IV. Answer Key
1. 5
2. 100
3. 1,331
4. 3/2
5. 1/1024
6. –1/6
7. 5
8. 1/7
9. 8
10. 0.2
11. a 2 3 a
12. z 2 5 z
13. 2cd 2 4 c
14. 3ab 3 b2
15. 3x 2 yz 4 5 xy 3
16. 2xy 2 3 x 2
17. bc 2 6 a 4 b2
18. 2de2 f 3 5d 2 f
19. m4 n2 p3 3 mn2
20. 2r 2 s3t 2 5 2r 3t 2
21. 4
22. 2401
23. The student did not write b on the outside of the radical.
24. (a) (–4)2/3 (b) 41/2
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