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Exponent Rules For Fractions - 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=factorGiven

Simplify the following to a reduced fraction. Answer in the form '5/9'. Use improper fractions instead of mixed fractions.

1.  
9
27
=
32
33
2.  
81
243
=
34
35

Complexity=5, Mode=factorNotGiven

Simplify the following to a reduced fraction. Answer in the form '5/9'. Use improper fractions instead of mixed fractions.

1.  
125
3125
2.  
2
8

Complexity=5, Mode=extraFactor

Simplify the following to a reduced fraction. Answer in the form '5/9'. Use improper fractions instead of mixed fractions.

1.  
40
4375
2.  
648
6561

Answers


Complexity=5, Mode=factorGiven

Simplify the following to a reduced fraction. Answer in the form '5/9'. Use improper fractions instead of mixed fractions.

#ProblemCorrect AnswerYour Answer
1
9
27
=
32
33
Solution

9
27
=
32
33
= 32 - 3 = 3-1 = 1/3
#ProblemCorrect AnswerYour Answer
2
81
243
=
34
35
Solution

81
243
=
34
35
= 34 - 5 = 3-1 = 1/3

Complexity=5, Mode=factorNotGiven

Simplify the following to a reduced fraction. Answer in the form '5/9'. Use improper fractions instead of mixed fractions.

#ProblemCorrect AnswerYour Answer
1
125
3125
Solution

125
3125
=
53
55
= 53 - 5 = 5-2 = 1/25
#ProblemCorrect AnswerYour Answer
2
2
8
Solution

2
8
=
21
23
= 21 - 3 = 2-2 = 1/4

Complexity=5, Mode=extraFactor

Simplify the following to a reduced fraction. Answer in the form '5/9'. Use improper fractions instead of mixed fractions.

#ProblemCorrect AnswerYour Answer
1
40
4375
Solution

40
4375
=
8 × 51
7 × 54
=
8
7
× 51 - 4 =
8
7
× 5-3 =
8
7
×
1
125
= 8/875
#ProblemCorrect AnswerYour Answer
2
648
6561
Solution

648
6561
=
8 × 34
9 × 36
=
8
9
× 34 - 6 =
8
9
× 3-2 =
8
9
×
1
9
= 8/81
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