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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.  
2
4
=
21
22
2.  
16
1024
=
42
45

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.  
16
1024
2.  
9
243

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.  
6
32
2.  
12
32

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
2
4
=
21
22
Solution

2
4
=
21
22
= 21 - 2 = 2-1 = 1/2
#ProblemCorrect AnswerYour Answer
2
16
1024
=
42
45
Solution

16
1024
=
42
45
= 42 - 5 = 4-3 = 1/64

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
16
1024
Solution

16
1024
=
42
45
= 42 - 5 = 4-3 = 1/64
#ProblemCorrect AnswerYour Answer
2
9
243
Solution

9
243
=
32
35
= 32 - 5 = 3-3 = 1/27

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
6
32
Solution

6
32
=
3 × 21
8 × 22
=
3
8
× 21 - 2 =
3
8
× 2-1 =
3
8
×
1
2
= 3/16
#ProblemCorrect AnswerYour Answer
2
12
32
Solution

12
32
=
6 × 21
4 × 23
=
6
4
× 21 - 3 =
6
4
× 2-2 =
6
4
×
1
4
= 3/8
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