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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 input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
1.  
( 1
5 		)
4
 
2.  
( 1
2 		)
4
 

Complexity=7, Mode=denominator

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
1.  
( 1
6 		)
3
 
2.  
( 4
5 		)
4
 

Complexity=10

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
1.  
( 3
4 		)
4
 
2.  
( 9
9 		)
3
 

Complexity=15

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
1.  
( 14
15 		)
3
 
2.  
( 10
12 		)
4
 

Answers

Complexity=5, Mode=1

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
#ProblemCorrect AnswerYour Answer
1
( 1
5 		)
4
 
Solution

( 1
5 		)
4
 
 =
( 14
54 		)
 


( 14
54 		)
 
 =
1
625
#ProblemCorrect AnswerYour Answer
2
( 1
2 		)
4
 
Solution

( 1
2 		)
4
 
 =
( 14
24 		)
 


( 14
24 		)
 
 =
1
16

Complexity=7, Mode=denominator

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
#ProblemCorrect AnswerYour Answer
1
( 1
6 		)
3
 
Solution

( 1
6 		)
3
 
 =
( 13
63 		)
 


( 13
63 		)
 
 =
1
216
#ProblemCorrect AnswerYour Answer
2
( 4
5 		)
4
 
Solution

( 4
5 		)
4
 
 =
( 44
54 		)
 


( 44
54 		)
 
 =
256
625

Complexity=10

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
#ProblemCorrect AnswerYour Answer
1
( 3
4 		)
4
 
Solution

( 3
4 		)
4
 
 =
( 34
44 		)
 


( 34
44 		)
 
 =
81
256
#ProblemCorrect AnswerYour Answer
2
( 9
9 		)
3
 
Solution
Begin by simplifying the fraction:

( 9
9 		)
3
 
 =
( 1
1 		)
3
 


( 1
1 		)
3
 
 =
( 13
13 		)
 


( 13
13 		)
 
 =
1
1

Complexity=15

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
#ProblemCorrect AnswerYour Answer
1
( 14
15 		)
3
 
Solution

( 14
15 		)
3
 
 =
( 143
153 		)
 


( 143
153 		)
 
 =
2744
3375
#ProblemCorrect AnswerYour Answer
2
( 10
12 		)
4
 
Solution
Begin by simplifying the fraction:

( 10
12 		)
4
 
 =
( 5
6 		)
4
 


( 5
6 		)
4
 
 =
( 54
64 		)
 


( 54
64 		)
 
 =
625
1296
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