## 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

### 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
Solution

( 1
3
)
 -1
= 1 ÷
( 1
3
)
 1

1 ÷
( 1
3
)
 1
=
( 3
1
)
 1

( 3
1
)
 1
=
 3111

 3111
=
 31
2
( 1
2
)
 -1
Solution

( 1
2
)
 -1
= 1 ÷
( 1
2
)
 1

1 ÷
( 1
2
)
 1
=
( 2
1
)
 1

( 2
1
)
 1
=
 2111

 2111
=
 21

### 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
Solution

( 5
7
)
 -3
= 1 ÷
( 5
7
)
 3

1 ÷
( 5
7
)
 3
=
( 7
5
)
 3

( 7
5
)
 3
=
 7353

 7353
=
 343125
2
( 4
7
)
 -2
Solution

( 4
7
)
 -2
= 1 ÷
( 4
7
)
 2

1 ÷
( 4
7
)
 2
=
( 7
4
)
 2

( 7
4
)
 2
=
 7242

 7242
=
 4916

### 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
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
=
 4333

 4333
=
 6427
2
( 1
7
)
 -4
Solution

( 1
7
)
 -4
= 1 ÷
( 1
7
)
 4

1 ÷
( 1
7
)
 4
=
( 7
1
)
 4

( 7
1
)
 4
=
 7414

 7414
=
 24011

### 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
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
=
 4232

 4232
=
 169
2
( 4
11
)
 -2
Solution

( 4
11
)
 -2
= 1 ÷
( 4
11
)
 2

1 ÷
( 4
11
)
 2
=
( 11
4
)
 2

( 11
4
)
 2
=
 11242

 11242
=
 12116