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Multiplying and Dividing Exponent Expressions - 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=multiply

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
1.   5 75 × 5 -78   Final Exponent: 5
  Value: 		2.   2 -16 × 2 13   Final Exponent: 2
  Value:

Complexity=5, Mode=divide

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
1.   3 -98 ÷ 3 -97   Final Exponent: 3
  Value: 		2.   3 94 ÷ 3 91   Final Exponent: 3
  Value:

Complexity=5, Mode=3

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
1.   4 -91 ÷ 4 51 × 4 142   Final Exponent: 4
  Value: 		2.   1 -45 × 1 -95 × 1 138   Final Exponent: 1
  Value:

Complexity=5, Mode=4

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
1.   2 -6 × 2 -44 ÷ 2 29 × 2 81   Final Exponent: 2
  Value: 		2.   2 -34 ÷ 2 -42 ÷ 2 -57 ÷ 2 68   Final Exponent: 2
  Value:

Complexity=5, Mode=5

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
1.   4 34 × 4 63 ÷ 4 -42 ÷ 4 14 × 4 -127   Final Exponent: 4
  Value: 		2.   3 66 ÷ 3 -63 ÷ 3 92 × 3 94 × 3 -128   Final Exponent: 3
  Value:

Answers

Complexity=5, Mode=multiply

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
#ProblemCorrect AnswerYour Answer
15 75 × 5 -78   Final Exponent: 5
  Value:
Solution
When you multiply two exponent expressions with the same common base, you can add the exponents.
Final exponent = 75 + -78 = -3
5 75 × 5 -78 = 5-3
5-3 = 1/125
#ProblemCorrect AnswerYour Answer
22 -16 × 2 13   Final Exponent: 2
  Value:
Solution
When you multiply two exponent expressions with the same common base, you can add the exponents.
Final exponent = -16 + 13 = -3
2 -16 × 2 13 = 2-3
2-3 = 1/8

Complexity=5, Mode=divide

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
#ProblemCorrect AnswerYour Answer
13 -98 ÷ 3 -97   Final Exponent: 3
  Value:
Solution
When you divide two exponent expressions with the same common base, you can subtract the exponents.
Final exponent = -98 - -97 = -1
3 -98 ÷ 3 -97 = 3-1
3-1 = 1/3
#ProblemCorrect AnswerYour Answer
23 94 ÷ 3 91   Final Exponent: 3
  Value:
Solution
When you divide two exponent expressions with the same common base, you can subtract the exponents.
Final exponent = 94 - 91 = 3
3 94 ÷ 3 91 = 33
33 = 27

Complexity=5, Mode=3

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
#ProblemCorrect AnswerYour Answer
14 -91 ÷ 4 51 × 4 142   Final Exponent: 4
  Value:
Solution
When you multiply two exponent expressions with the same common base, you can add the exponents.
When you divide two exponent expressions with the same common base, you can subtract the exponents.
Final exponent = -91 - 51 + 142 = 0
4 -91 ÷ 4 51 × 4 142 = 40
40 = 1
#ProblemCorrect AnswerYour Answer
21 -45 × 1 -95 × 1 138   Final Exponent: 1
  Value:
Solution
When you multiply two exponent expressions with the same common base, you can add the exponents.
When you divide two exponent expressions with the same common base, you can subtract the exponents.
Final exponent = -45 + -95 + 138 = -2
1 -45 × 1 -95 × 1 138 = 1-2
1-2 = 1

Complexity=5, Mode=4

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
#ProblemCorrect AnswerYour Answer
12 -6 × 2 -44 ÷ 2 29 × 2 81   Final Exponent: 2
  Value:
Solution
When you multiply two exponent expressions with the same common base, you can add the exponents.
When you divide two exponent expressions with the same common base, you can subtract the exponents.
Final exponent = -6 + -44 - 29 + 81 = 2
2 -6 × 2 -44 ÷ 2 29 × 2 81 = 22
22 = 4
#ProblemCorrect AnswerYour Answer
22 -34 ÷ 2 -42 ÷ 2 -57 ÷ 2 68   Final Exponent: 2
  Value:
Solution
When you multiply two exponent expressions with the same common base, you can add the exponents.
When you divide two exponent expressions with the same common base, you can subtract the exponents.
Final exponent = -34 - -42 - -57 - 68 = -3
2 -34 ÷ 2 -42 ÷ 2 -57 ÷ 2 68 = 2-3
2-3 = 1/8

Complexity=5, Mode=5

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'
#ProblemCorrect AnswerYour Answer
14 34 × 4 63 ÷ 4 -42 ÷ 4 14 × 4 -127   Final Exponent: 4
  Value:
Solution
When you multiply two exponent expressions with the same common base, you can add the exponents.
When you divide two exponent expressions with the same common base, you can subtract the exponents.
Final exponent = 34 + 63 - -42 - 14 + -127 = -2
4 34 × 4 63 ÷ 4 -42 ÷ 4 14 × 4 -127 = 4-2
4-2 = 1/16
#ProblemCorrect AnswerYour Answer
23 66 ÷ 3 -63 ÷ 3 92 × 3 94 × 3 -128   Final Exponent: 3
  Value:
Solution
When you multiply two exponent expressions with the same common base, you can add the exponents.
When you divide two exponent expressions with the same common base, you can subtract the exponents.
Final exponent = 66 - -63 - 92 + 94 + -128 = 3
3 66 ÷ 3 -63 ÷ 3 92 × 3 94 × 3 -128 = 33
33 = 27
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