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Negative 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
3 		)
-1
 
2.  
( 1
2 		)
-1
 

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.  
( 5
7 		)
-3
 
2.  
( 4
7 		)
-2
 

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.  
( 6
8 		)
-3
 
2.  
( 1
7 		)
-4
 

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.  
( 6
8 		)
-2
 
2.  
( 4
11 		)
-2
 

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
3 		)
-1
 
Solution

( 1
3 		)
-1
 
 = 1 ÷
( 1
3 		)
1
 

1 ÷
( 1
3 		)
1
 
 =
( 3
1 		)
1
 

( 3
1 		)
1
 
 =
31
11


31
11
=
3
1
#ProblemCorrect AnswerYour Answer
2
( 1
2 		)
-1
 
Solution

( 1
2 		)
-1
 
 = 1 ÷
( 1
2 		)
1
 

1 ÷
( 1
2 		)
1
 
 =
( 2
1 		)
1
 

( 2
1 		)
1
 
 =
21
11


21
11
=
2
1

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
( 5
7 		)
-3
 
Solution

( 5
7 		)
-3
 
 = 1 ÷
( 5
7 		)
3
 

1 ÷
( 5
7 		)
3
 
 =
( 7
5 		)
3
 

( 7
5 		)
3
 
 =
73
53


73
53
=
343
125
#ProblemCorrect AnswerYour Answer
2
( 4
7 		)
-2
 
Solution

( 4
7 		)
-2
 
 = 1 ÷
( 4
7 		)
2
 

1 ÷
( 4
7 		)
2
 
 =
( 7
4 		)
2
 

( 7
4 		)
2
 
 =
72
42


72
42
=
49
16

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
( 6
8 		)
-3
 
Solution

( 6
8 		)
-3
 
 = 1 ÷
( 6
8 		)
3
 

1 ÷
( 6
8 		)
3
 
 =
( 8
6 		)
3
 
Simplify the fraction:

( 8
6 		)
3
 
 =
( 4
3 		)
3
 


( 4
3 		)
3
 
 =
43
33


43
33
=
64
27
#ProblemCorrect AnswerYour Answer
2
( 1
7 		)
-4
 
Solution

( 1
7 		)
-4
 
 = 1 ÷
( 1
7 		)
4
 

1 ÷
( 1
7 		)
4
 
 =
( 7
1 		)
4
 

( 7
1 		)
4
 
 =
74
14


74
14
=
2401
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
( 6
8 		)
-2
 
Solution

( 6
8 		)
-2
 
 = 1 ÷
( 6
8 		)
2
 

1 ÷
( 6
8 		)
2
 
 =
( 8
6 		)
2
 
Simplify the fraction:

( 8
6 		)
2
 
 =
( 4
3 		)
2
 


( 4
3 		)
2
 
 =
42
32


42
32
=
16
9
#ProblemCorrect AnswerYour Answer
2
( 4
11 		)
-2
 
Solution

( 4
11 		)
-2
 
 = 1 ÷
( 4
11 		)
2
 

1 ÷
( 4
11 		)
2
 
 =
( 11
4 		)
2
 

( 11
4 		)
2
 
 =
112
42


112
42
=
121
16
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