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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is a proficiency exam to the chapter "Exponents, Roots, Factorization of Whole Numbers." Each problem is accompanied with a reference link pointing back to the module that discusses the type of problem demonstrated in the question. The problems in this exam are accompanied by solutions.

Proficiency exam

( [link] ) In the number 8 5 , write the names used for the number 8 and the number 5.

base; exponent

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( [link] ) Write using exponents. 12 × 12 × 12 × 12 × 12 × 12 × 12 size 12{"12" times "12" times "12" times "12" times "12" times "12" times "12"} {}

12 7 size 12{"12" rSup { size 8{7} } } {}

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( [link] ) Expand 9 4 size 12{9 rSup { size 8{4} } } {} .

9 4 = 9 9 9 9 = 6, 561 size 12{9 rSup { size 8{4} } =9 cdot 9 cdot 9 cdot 9=6,"561"} {}

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For problems 4-15, determine the value of each expression.

( [link] ) 4 3 size 12{4 rSup { size 8{3} } } {}

64

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( [link] ) 1 5 size 12{1 rSup { size 8{5} } } {}

1

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( [link] ) 0 3 size 12{0 rSup { size 8{3} } } {}

0

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( [link] ) 2 6 size 12{2 rSup { size 8{6} } } {}

64

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( [link] ) 49 size 12{ sqrt {"49"} } {}

7

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( [link] ) 27 3 size 12{ nroot { size 8{3} } {"27"} } {}

3

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( [link] ) 1 8 size 12{ nroot { size 8{8} } {1} } {}

1

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( [link] ) 16 + 2 ( 8 6 ) size 12{"16"+2 cdot \( 8 - 6 \) } {}

20

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( [link] ) 5 3 100 + 8 2 20 ÷ 5 size 12{5 rSup { size 8{3} } - sqrt {"100"} +8 cdot 2 - "20" div 5} {}

127

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( [link] ) 3 8 2 2 3 2 5 2 2 6 3 4 5 2 29 size 12{3 cdot { {8 rSup { size 8{2} } - 2 cdot 3 rSup { size 8{2} } } over {5 rSup { size 8{2} } - 2} } cdot { {6 rSup { size 8{3} } - 4 cdot 5 rSup { size 8{2} } } over {"29"} } } {}

24

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( [link] ) 20 + 2 4 2 3 2 5 2 5 7 - 81 7 + 3 2 size 12{ { {"20"+2 rSup { size 8{4} } } over {2 rSup { size 8{3} } cdot 2 - 5 cdot 2} } cdot { {6 rSup { size 8{3} } - 4 cdot 5 rSup { size 8{2} } } over {"29"} } } {}

8

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( [link] ) 8 3 2 + 33 4 49 2 10 3 2 + 9 5 size 12{ left [ left (8 - 3 right ) rSup { size 8{2} } + left ("33" - 4 sqrt {"49"} right ) right ] - 2 left [ left ("10" - 3 rSup { size 8{2} } right )+9 right ]- 5} {}

5

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For problems 16-20, find the prime factorization of each whole number. If the number is prime, write "prime."

( [link] ) 18

3 2 2 size 12{3 rSup { size 8{2} } cdot 2} {}

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( [link] ) 68

2 2 17 size 12{2 rSup { size 8{2} } cdot "17"} {}

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( [link] ) 142

2 71 size 12{2 cdot "71"} {}

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( [link] ) 468

2 2 3 2 13 size 12{2 rSup { size 8{2} } cdot 3"" lSup { size 8{2} } cdot "13"} {}

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For problems 21 and 22, find the greatest common factor.

( [link] ) Write all the factors of 36.

1, 2, 3, 4, 6, 9, 12, 18, 36

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( [link] ) Write all the divisors of 18.

1, 2, 3, 6, 9, 18

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( [link] ) Does 7 divide into 5 2 6 3 7 4 8 size 12{5 rSup { size 8{2} } cdot 6 rSup { size 8{3} } cdot 7 rSup { size 8{4} } cdot 8} {} ? Explain.

Yes, because one of the (prime) factors of the number is 7.

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( [link] ) Is 3 a factor of 2 6 3 2 5 3 4 6 size 12{2 rSup { size 8{6} } cdot 3 rSup { size 8{2} } cdot 5 rSup { size 8{3} } cdot 4 rSup { size 8{6} } } {} ? Explain.

Yes, because it is one of the factors of the number.

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( [link] ) Does 13 divide into 11 3 12 4 15 2 size 12{"11" rSup { size 8{3} } cdot "12" rSup { size 8{4} } cdot "15" rSup { size 8{2} } } {} ? Explain.

No, because the prime 13 is not a factor any of the listed factors of the number.

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For problems 28 and 29, find the least common multiple.

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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