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For problems 1 -25, determine the value of each power and root.
${4}^{3}$
${1}^{4}$
${7}^{2}$
${\text{11}}^{2}$
${3}^{4}$
${\text{20}}^{2}$
$\sqrt{\text{36}}$
$\sqrt[3]{\text{64}}$
$\sqrt{0}$
$\sqrt[3]{\text{216}}$
$\sqrt{\text{196}}$
$\sqrt[4]{0}$
For problems 26-45, use the order of operations to determine each value.
${2}^{3}-2\cdot 4$
$\sqrt{\text{81}}-{3}^{2}+6\cdot 2$
$3\cdot \left({2}^{2}+{3}^{2}\right)$
$\frac{{5}^{2}+1}{\text{13}}+\frac{{3}^{3}+1}{\text{14}}$
$\frac{{6}^{2}-1}{5\cdot 7}-\frac{\text{49}+7}{2\cdot 7}$
-3
$\frac{2\cdot \left[3+5\left({2}^{2}+1\right)\right]}{5\cdot {2}^{3}-{3}^{2}}$
$\frac{{3}^{2}\cdot \left[{2}^{5}-{1}^{4}\left({2}^{3}+\text{25}\right)\right]}{2\cdot {5}^{2}+5+2}$
$-\frac{9}{\text{57}}$
$\frac{\left({5}^{2}-{2}^{3}\right)-2\cdot 7}{{2}^{2}-1}+5\cdot \left[\frac{{3}^{2}-3}{2}+1\right]$
${3}^{2}\cdot \left({4}^{2}+\sqrt{\text{25}}\right)+{2}^{3}\cdot \left(\sqrt{\text{81}}-{3}^{2}\right)$
$\sqrt{\text{16}}+\sqrt{9}$
Compare the results of problems 39 and 40. What might we conclude?
The sum of square roots is not necessarily equal to the square root of the sum.
$\sqrt{\text{18}\cdot 2}$
$\sqrt{7\cdot 7}$
An
For problems 47- 53, find all the factors of each number.
What number is the smallest prime number?
For problems 55 -64, write each number as a product of prime factors.
For problems 65 - 75, find the greatest common factor of each collection of numbers.
6, 8, and 12
42 and 54
18, 48, and 72
64, 72, and 108
For problems 76-86, find the least common multiple of each collection of numbers.
10 and 15
42 and 54
40, 50, and 180
108, 144, and 324
12, 15, 18, and 20
Find all factors of 24.
Write all divisors of ${2}^{3}\cdot {5}^{2}\cdot 7$ .
1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 700, 1,400
Write all divisors of $6\cdot {8}^{2}\cdot {\text{10}}^{3}$ .
Does 7 divide ${5}^{3}\cdot {6}^{4}\cdot {7}^{2}\cdot {8}^{5}$ ?
yes
Does 13 divide ${8}^{3}\cdot {\text{10}}^{2}\cdot {\text{11}}^{4}\cdot {\text{13}}^{2}\cdot \text{15}$ ?
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