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Exponents Of Fractional Bases - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=5, Mode=1

Evaluate the following. If the answer is a whole number, just give the whole number. For fractions, express as 'numerator/denominator'. i.e. '5/7'. Also, use improper fractions -- not mixed fractions -- in your answer.

1.  
( 1
2 		)
3
 
2.  
( 1
4 		)
4
 

Complexity=7, Mode=denominator

Evaluate the following. If the answer is a whole number, just give the whole number. For fractions, express as 'numerator/denominator'. i.e. '5/7'. Also, use improper fractions -- not mixed fractions -- in your answer.

1.  
( 2
6 		)
3
 
2.  
( 1
6 		)
4
 

Complexity=10

Evaluate the following. If the answer is a whole number, just give the whole number. For fractions, express as 'numerator/denominator'. i.e. '5/7'. Also, use improper fractions -- not mixed fractions -- in your answer.

1.  
( 6
7 		)
4
 
2.  
( 8
4 		)
2
 

Complexity=15

Evaluate the following. If the answer is a whole number, just give the whole number. For fractions, express as 'numerator/denominator'. i.e. '5/7'. Also, use improper fractions -- not mixed fractions -- in your answer.

1.  
( 10
8 		)
2
 
2.  
( 11
10 		)
4
 

Answers

Complexity=5, Mode=1

Evaluate the following. If the answer is a whole number, just give the whole number. For fractions, express as 'numerator/denominator'. i.e. '5/7'. Also, use improper fractions -- not mixed fractions -- in your answer.

#ProblemCorrect AnswerYour Answer
1
( 1
2 		)
3
 
Solution

( 1
2 		)
3
 
 =
( 13
23 		)
 


( 13
23 		)
 
 =
1
8
#ProblemCorrect AnswerYour Answer
2
( 1
4 		)
4
 
Solution

( 1
4 		)
4
 
 =
( 14
44 		)
 


( 14
44 		)
 
 =
1
256

Complexity=7, Mode=denominator

Evaluate the following. If the answer is a whole number, just give the whole number. For fractions, express as 'numerator/denominator'. i.e. '5/7'. Also, use improper fractions -- not mixed fractions -- in your answer.

#ProblemCorrect AnswerYour Answer
1
( 2
6 		)
3
 
Solution
Begin by simplifying the fraction:

( 2
6 		)
3
 
 =
( 1
3 		)
3
 


( 1
3 		)
3
 
 =
( 13
33 		)
 


( 13
33 		)
 
 =
1
27
#ProblemCorrect AnswerYour Answer
2
( 1
6 		)
4
 
Solution

( 1
6 		)
4
 
 =
( 14
64 		)
 


( 14
64 		)
 
 =
1
1296

Complexity=10

Evaluate the following. If the answer is a whole number, just give the whole number. For fractions, express as 'numerator/denominator'. i.e. '5/7'. Also, use improper fractions -- not mixed fractions -- in your answer.

#ProblemCorrect AnswerYour Answer
1
( 6
7 		)
4
 
Solution

( 6
7 		)
4
 
 =
( 64
74 		)
 


( 64
74 		)
 
 =
1296
2401
#ProblemCorrect AnswerYour Answer
2
( 8
4 		)
2
 
Solution
Begin by simplifying the fraction:

( 8
4 		)
2
 
 =
( 2
1 		)
2
 


( 2
1 		)
2
 
 =
( 22
12 		)
 


( 22
12 		)
 
 =
4
1

Complexity=15

Evaluate the following. If the answer is a whole number, just give the whole number. For fractions, express as 'numerator/denominator'. i.e. '5/7'. Also, use improper fractions -- not mixed fractions -- in your answer.

#ProblemCorrect AnswerYour Answer
1
( 10
8 		)
2
 
Solution
Begin by simplifying the fraction:

( 10
8 		)
2
 
 =
( 5
4 		)
2
 


( 5
4 		)
2
 
 =
( 52
42 		)
 


( 52
42 		)
 
 =
25
16
#ProblemCorrect AnswerYour Answer
2
( 11
10 		)
4
 
Solution

( 11
10 		)
4
 
 =
( 114
104 		)
 


( 114
104 		)
 
 =
14641
10000
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