3.10: Exercise Supplement
- Page ID
- 58493
Exercise Supplement
Signed Numbers
For the following problems, find \(−a\) if \(a\) is
how many exercises?
\(27\)
- Answer
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\(-27\)
\(-15\)
\(-\dfrac{8}{9}\)
- Answer
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\(\dfrac{8}{9}\)
\(-(-3)\)
\(k\)
- Answer
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\(-k\)
Absolute Value
Simplify the following problems.
\(|8|\)
\(|-3|\)
- Answer
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\(3\)
\(-|16|\)
\(-(-|12|)\)
- Answer
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\(12\)
\(-|0|\)
Addition of Signed Numbers - Multiplication and Division of Signed Numbers
Simplify the following problems.
\(4 + (-6)\)
- Answer
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\(-2\)
\(-16 + (-18)\)
\(3 - (-14)\)
- Answer
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\(17\)
\((-5)(2)\)
\((-6)(-3)\)
- Answer
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\(18\)
\((-1)(-4)\)
\((4)(-3)\)
- Answer
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\(-12\)
\(\dfrac{-25}{5}\)
\(\dfrac{-100}{-10}\)
- Answer
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\(10\)
\(16 - 18 + 5\)
\(\dfrac{(-2)(-4) + 10}{-5}\)
- Answer
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\(-\dfrac{18}{5}\)
\(\dfrac{-3(-8+4)-12}{4(3+6)-2(-8)}\)
\(\dfrac{-1(-3-2)-4(-4)}{-13+10}\)
- Answer
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\(-7\)
\(-(2-10)\)
\(0 - 6(-4)(-2)\)
- Answer
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\(-48\)
Multiplication and Division of Signed Numbers
Find the value of each expression for the following problems.
\(P = R - C\). Find \(P\) if \(R = 3000\) and \(C = 3800\).
\(z = \dfrac{x-u}{s}\). Find \(z\) if \(x = 22, u = 30\), and \(s = 8\).
- Answer
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\(-1\)
\(P = n(n-1)(n-2)\). Find \(P\) if \(n = -3\).
Negative Exponents
Write the expressions for the following problems using only positive exponents.
\(a^{-1}\)
- Answer
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\(\dfrac{1}{a}\)
\(c^{-6}\)
\(a^3b^{-2}c^{-5}\)
- Answer
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\(\dfrac{a^3}{b^2c^5}\)
\((x+5)^{-2}\)
\(x^3y^2(x-3)^{-7}\)
- Answer
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\(\dfrac{x^3y^2}{(x-3)^7}\)
\(4^{-2}a^{-3}b^{-4}c^5\)
\(2^{-1}x^{-1}\)
- Answer
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\(\dfrac{1}{2x}\)
\((2x+9)^{-3}7x^4y^{-5}z^{-2}(3x-1)^2(2x+5)^{-1}\)
\((-2)^{-1}\)
- Answer
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\(\dfrac{1}{-2}\)
\(\dfrac{1}{x^{-4}}\)
\(\dfrac{7x}{y^{-3}z^{-2}}\)
- Answer
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\(7xy^3z^2\)
\(\dfrac{4c^{-2}}{b^{-6}}\)
\(\dfrac{3^{-2}a^{-5}b^{-9}c^2}{x^2y^{-4}z^{-1}}\)
- Answer
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\(\dfrac{c^2y^4z}{9a^5b^9x^2}\)
\(\dfrac{(z-6)^{-2}}{(z+6)^{-4}}\)
\(\dfrac{16a^5b^{-2}}{-2a^3b^{-5}}\)
- Answer
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\(-8a^2b^3\)
\(\dfrac{-44x^3y^{-6}z^{-8}}{-11x^{-2}y^{-7}z^{-8}}\)
\(8^{-2}\)
- Answer
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\(\dfrac{1}{64}\)
\(9^{-1}\)
\(2^{-5}\)
- Answer
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\(\dfrac{1}{32}\)
\((x^3)^{-2}\)
\((a^2b)^{-3}\)
- Answer
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\(\dfrac{1}{a^6b^3}\)
\((x^{-2})^{-4}\)
\((c^{-1})^{-4}\)
- Answer
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\(c^4\)
\((y^{-1})^{-1}\)
\((x^3y^{-4}z^{-2})^{-6}\)
- Answer
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\(\dfrac{y^{24}z^{12}}{x^{18}}\)
\((\dfrac{x^{-6}}{y^{-2}})^{-5}\)
\((\dfrac{2b^{-7}c^{-8}d^4}{x^{-2}y^3z})^{-4}\)
- Answer
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\(\dfrac{b^{28}c^{32}y^{12}z^4}{16d^{16}x^8}\)
Scientific Notation
Write the following problems using scientific not
8739
73567
- Answer
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\(7.3567 \times 10^4\)
21,000
746,000
- Answer
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\(7.46 \times 10^5\)
8866846
0.0387
- Answer
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\(3.87 \times 10^{-2}\)
0.0097
0.376
- Answer
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\(3.76 \times 10^{-1}\)
0.0000024
0.000000000000537
- Answer
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\(5.37 \times 10^{-13}\)
46,000,000,000,000,000
Convert the following problems from scientific form to standard form.
\(3.87 \times 10^5\)
- Answer
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387,000
\(4.145 \times 10^4\)
\(6.009 \times 10^7\)
- Answer
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60,090,000
\(1.80067 \times 10^6\)
\(3.88 \times 10^{-5}\)
- Answer
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0.0000388
\(4.116 \times 10^{-2}\)
\(8.002 \times 10^{-12}\)
- Answer
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0.000000000008002
\(7.36490 \times 10^{-14}\)
\(2.101 \times 10^{15}\)
- Answer
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2,101,000,000,000,000
\(6.7202 \times 10^{26}\)
\(1 \times 10^6\)
- Answer
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1,000,000
\(1 \times 10^7\)
\(1 \times 10^9\)
- Answer
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1,000,000,000
Find the product for the following problems. Write the result in scientific notation.
\((1 \times 10^5)(2 \times 10^3)\)
\((3 \times 10^6)(7 \times 10^7)\)
- Answer
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\(2.1 \times 10^{14}\)
\((9 \times 10^2)(3 \times 10^{75})\)
- Answer
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\(2.7 \times 10^{78}\)
\((1 \times 10^4)(1 \times 10^5)\)
\((8 \times 10^{-3})(3 \times 10^{-6})\)
- Answer
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\(2.4 \times 10^{-8}\)
\(9 \times 10^{-5})(2 \times 10^{-1})\)
\((3 \times 10^{-2})(7 \times 10^2)\)
- Answer
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\(2.1 \times 10^1\)
\((7.3 \times 10^4)(2.1 \times 10^{-8})\)
\((1.06 \times 10^{-16})(2.815 \times 10^{-12})\)
- Answer
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\(2.9839 \times 10^{-28}\)
\((9.3806 \times 10^{52})(1.009 \times 10^{-31})\)