3.10: Exercise Supplement

Exercise Supplement

Signed Numbers

For the following problems, find $−a$ if $a$ is

how many exercises?

Exercise $\PageIndex{1}$

$27$

Answer

$-27$

Exercise $\PageIndex{2}$

$-15$

Exercise $\PageIndex{3}$

$-\dfrac{8}{9}$

Answer

$\dfrac{8}{9}$

Exercise $\PageIndex{4}$

$-(-3)$

Exercise $\PageIndex{5}$

$k$

Answer

$-k$

Absolute Value

Simplify the following problems.

Exercise $\PageIndex{6}$

$|8|$

Exercise $\PageIndex{7}$

$|-3|$

Answer

$3$

Exercise $\PageIndex{8}$

$-|16|$

Exercise $\PageIndex{9}$

$-(-|12|)$

Answer

$12$

Exercise $\PageIndex{10}$

$-|0|$

Addition of Signed Numbers - Multiplication and Division of Signed Numbers

Simplify the following problems.

Exercise $\PageIndex{11}$

$4 + (-6)$

Answer

$-2$

Exercise $\PageIndex{12}$

$-16 + (-18)$

Exercise $\PageIndex{13}$

$3 - (-14)$

Answer

$17$

Exercise $\PageIndex{14}$

$(-5)(2)$

Exercise $\PageIndex{15}$

$(-6)(-3)$

Answer

$18$

Exercise $\PageIndex{16}$

$(-1)(-4)$

Exercise $\PageIndex{17}$

$(4)(-3)$

Answer

$-12$

Exercise $\PageIndex{18}$

$\dfrac{-25}{5}$

Exercise $\PageIndex{19}$

$\dfrac{-100}{-10}$

Answer

$10$

Exercise $\PageIndex{20}$

$16 - 18 + 5$

Exercise $\PageIndex{21}$

$\dfrac{(-2)(-4) + 10}{-5}$

Answer

$-\dfrac{18}{5}$

Exercise $\PageIndex{22}$

$\dfrac{-3(-8+4)-12}{4(3+6)-2(-8)}$

Exercise $\PageIndex{23}$

$\dfrac{-1(-3-2)-4(-4)}{-13+10}$

Answer

$-7$

Exercise $\PageIndex{24}$

$-(2-10)$

Exercise $\PageIndex{25}$

$0 - 6(-4)(-2)$

Answer

$-48$

Multiplication and Division of Signed Numbers

Find the value of each expression for the following problems.

Exercise $\PageIndex{26}$

$P = R - C$. Find $P$ if $R = 3000$ and $C = 3800$.

Exercise $\PageIndex{27}$

$z = \dfrac{x-u}{s}$. Find $z$ if $x = 22, u = 30$, and $s = 8$.

Answer

$-1$

Exercise $\PageIndex{28}$

$P = n(n-1)(n-2)$. Find $P$ if $n = -3$.

Negative Exponents

Write the expressions for the following problems using only positive exponents.

Exercise $\PageIndex{29}$

$a^{-1}$

Answer

$\dfrac{1}{a}$

Exercise $\PageIndex{30}$

$c^{-6}$

Exercise $\PageIndex{31}$

$a^3b^{-2}c^{-5}$

Answer

$\dfrac{a^3}{b^2c^5}$

Exercise $\PageIndex{32}$

$(x+5)^{-2}$

Exercise $\PageIndex{33}$

$x^3y^2(x-3)^{-7}$

Answer

$\dfrac{x^3y^2}{(x-3)^7}$

Exercise $\PageIndex{34}$

$4^{-2}a^{-3}b^{-4}c^5$

Exercise $\PageIndex{35}$

$2^{-1}x^{-1}$

Answer

$\dfrac{1}{2x}$

Exercise $\PageIndex{36}$

$(2x+9)^{-3}7x^4y^{-5}z^{-2}(3x-1)^2(2x+5)^{-1}$

Exercise $\PageIndex{37}$

$(-2)^{-1}$

Answer

$\dfrac{1}{-2}$

Exercise $\PageIndex{38}$

$\dfrac{1}{x^{-4}}$

Exercise $\PageIndex{39}$

$\dfrac{7x}{y^{-3}z^{-2}}$

Answer

$7xy^3z^2$

Exercise $\PageIndex{40}$

$\dfrac{4c^{-2}}{b^{-6}}$

Exercise $\PageIndex{41}$

$\dfrac{3^{-2}a^{-5}b^{-9}c^2}{x^2y^{-4}z^{-1}}$

Answer

$\dfrac{c^2y^4z}{9a^5b^9x^2}$

Exercise $\PageIndex{42}$

$\dfrac{(z-6)^{-2}}{(z+6)^{-4}}$

Exercise $\PageIndex{43}$

$\dfrac{16a^5b^{-2}}{-2a^3b^{-5}}$

Answer

$-8a^2b^3$

Exercise $\PageIndex{44}$

$\dfrac{-44x^3y^{-6}z^{-8}}{-11x^{-2}y^{-7}z^{-8}}$

Exercise $\PageIndex{45}$

$8^{-2}$

Answer

$\dfrac{1}{64}$

Exercise $\PageIndex{46}$

$9^{-1}$

Exercise $\PageIndex{47}$

$2^{-5}$

Answer

$\dfrac{1}{32}$

Exercise $\PageIndex{48}$

$(x^3)^{-2}$

Exercise $\PageIndex{49}$

$(a^2b)^{-3}$

Answer

$\dfrac{1}{a^6b^3}$

Exercise $\PageIndex{50}$

$(x^{-2})^{-4}$

Exercise $\PageIndex{51}$

$(c^{-1})^{-4}$

Answer

$c^4$

Exercise $\PageIndex{52}$

$(y^{-1})^{-1}$

Exercise $\PageIndex{53}$

$(x^3y^{-4}z^{-2})^{-6}$

Answer

$\dfrac{y^{24}z^{12}}{x^{18}}$

Exercise $\PageIndex{54}$

$(\dfrac{x^{-6}}{y^{-2}})^{-5}$

Exercise $\PageIndex{55}$

$(\dfrac{2b^{-7}c^{-8}d^4}{x^{-2}y^3z})^{-4}$

Answer

$\dfrac{b^{28}c^{32}y^{12}z^4}{16d^{16}x^8}$

Scientific Notation

Write the following problems using scientific not

Exercise $\PageIndex{56}$

8739

Exercise $\PageIndex{57}$

73567

Answer

$7.3567 \times 10^4$

Exercise $\PageIndex{58}$

21,000

Exercise $\PageIndex{59}$

746,000

Answer

$7.46 \times 10^5$

Exercise $\PageIndex{60}$

8866846

Exercise $\PageIndex{61}$

0.0387

Answer

$3.87 \times 10^{-2}$

Exercise $\PageIndex{62}$

0.0097

Exercise $\PageIndex{63}$

0.376

Answer

$3.76 \times 10^{-1}$

Exercise $\PageIndex{64}$

0.0000024

Exercise $\PageIndex{65}$

0.000000000000537

Answer

$5.37 \times 10^{-13}$

Exercise $\PageIndex{66}$

46,000,000,000,000,000

Convert the following problems from scientific form to standard form.

Exercise $\PageIndex{67}$

$3.87 \times 10^5$

Answer

387,000

Exercise $\PageIndex{68}$

$4.145 \times 10^4$

Exercise $\PageIndex{69}$

$6.009 \times 10^7$

Answer

60,090,000

Exercise $\PageIndex{70}$

$1.80067 \times 10^6$

Exercise $\PageIndex{71}$

$3.88 \times 10^{-5}$

Answer

0.0000388

Exercise $\PageIndex{72}$

$4.116 \times 10^{-2}$

Exercise $\PageIndex{73}$

$8.002 \times 10^{-12}$

Answer

0.000000000008002

Exercise $\PageIndex{74}$

$7.36490 \times 10^{-14}$

Exercise $\PageIndex{75}$

$2.101 \times 10^{15}$

Answer

2,101,000,000,000,000

Exercise $\PageIndex{76}$

$6.7202 \times 10^{26}$

Exercise $\PageIndex{77}$

$1 \times 10^6$

Answer

1,000,000

Exercise $\PageIndex{78}$

$1 \times 10^7$

Exercise $\PageIndex{79}$

$1 \times 10^9$

Answer

1,000,000,000

Find the product for the following problems. Write the result in scientific notation.

Exercise $\PageIndex{80}$

$(1 \times 10^5)(2 \times 10^3)$

Exercise $\PageIndex{81}$

$(3 \times 10^6)(7 \times 10^7)$

Answer

$2.1 \times 10^{14}$

Exercise $\PageIndex{82}$

$(9 \times 10^2)(3 \times 10^{75})$

Answer

$2.7 \times 10^{78}$

Exercise $\PageIndex{83}$

$(1 \times 10^4)(1 \times 10^5)$

Exercise $\PageIndex{84}$

$(8 \times 10^{-3})(3 \times 10^{-6})$

Answer

$2.4 \times 10^{-8}$

Exercise $\PageIndex{85}$

$9 \times 10^{-5})(2 \times 10^{-1})$

Exercise $\PageIndex{86}$

$(3 \times 10^{-2})(7 \times 10^2)$

Answer

$2.1 \times 10^1$

Exercise $\PageIndex{87}$

$(7.3 \times 10^4)(2.1 \times 10^{-8})$

Exercise $\PageIndex{88}$

$(1.06 \times 10^{-16})(2.815 \times 10^{-12})$

Answer

$2.9839 \times 10^{-28}$

Exercise $\PageIndex{89}$

$(9.3806 \times 10^{52})(1.009 \times 10^{-31})$