Chapter 6 Review Exercises

Chapter 6 Review Exercises

Add and Subtract Polynomials

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

Exercise $\PageIndex{1}$

1. $11 c^{4}-23 c^{2}+1$
2. $9 p^{3}+6 p^{2}-p-5$
3. $\frac{3}{7} x+\frac{5}{14}$
4. 10
5. 2y−12

Exercise $\PageIndex{2}$

1. $a^{2}-b^{2}$
2. 24$d^{3}$
3. $x^{2}+8 x-10$
4. $m^{2} n^{2}-2 m n+6$
5. $7 y^{3}+y^{2}-2 y-4$

Answer

1. binomial
2. monomial
3. trinomial
4. trinomial
5. other polynomial

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

Exercise $\PageIndex{3}$

1. $3 x^{2}+9 x+10$
2. 14$a^{2} b c$
3. 6y+1
4. $n^{3}-4 n^{2}+2 n-8$
5. −19

Exercise $\PageIndex{4}$

1. $5 p^{3}-8 p^{2}+10 p-4$
2. $-20 q^{4}$
3. $x^{2}+6 x+12$
4. $23 r^{2} s^{2}-4 r s+5$
5. 100

Answer

1. 3
2. 4
3. 2
4. 4
5. 0

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

Exercise $\PageIndex{5}$

$5 y^{3}+8 y^{3}$

Exercise $\PageIndex{6}$

$-14 k+19 k$

Answer

5k

Exercise $\PageIndex{7}$

12q−(−6q)

Exercise $\PageIndex{8}$

−9c−18c

Answer

−27c

Exercise $\PageIndex{9}$

12x−4y−9x

Exercise $\PageIndex{2}$

$3 m^{2}+7 n^{2}-3 m^{2}$

Answer

7$n^{2}$

Exercise $\PageIndex{3}$

$6 x^{2} y-4 x+8 x y^{2}$

Exercise $\PageIndex{4}$

13a+b

Answer

13a+b

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

Exercise $\PageIndex{5}$

$\left(5 x^{2}+12 x+1\right)+\left(6 x^{2}-8 x+3\right)$

Exercise $\PageIndex{6}$

$\left(9 p^{2}-5 p+3\right)+\left(4 p^{2}-4\right)$

Answer

$13 p^{2}-5 p-1$

Exercise $\PageIndex{7}$

$\left(10 m^{2}-8 m-1\right)-\left(5 m^{2}+m-2\right)$

Exercise $\PageIndex{8}$

$\left(7 y^{2}-8 y\right)-(y-4)$

Answer

$7 y^{2}-9 y+4$

Exercise $\PageIndex{9}$

Subtract
$\left(3 s^{2}+10\right)$ from $\left(15 s^{2}-2 s+8\right)$

Exercise $\PageIndex{10}$

Find the sum of $\left(a^{2}+6 a+9\right)$ and $\left(5 a^{3}-7\right)$

Answer

$5 a^{3}+a^{2}+6 a+2$

Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

Exercise $\PageIndex{11}$

Evaluate $3 y^{2}-y+1$ when:

1. y=5
2. y=−1
3. y=0

Exercise $\PageIndex{12}$

Evaluate 10−12x when:

1. x=3
2. x=0
3. x=−1

Answer

1. −26
2. 10
3. 22

Exercise $\PageIndex{13}$

Randee drops a stone off the 200 foot high cliff into the ocean. The polynomial $-16 t^{2}+200$ gives the height of a stone t seconds after it is dropped from the cliff. Find the height after t=3 seconds.

Exercise $\PageIndex{14}$

A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial $-4 p^{2}+460 p$. Find the revenue received when p=75 dollars.

Answer

12,000

Use Multiplication Properties of Exponents

Simplify Expressions with Exponents

In the following exercises, simplify.

Exercise $\PageIndex{15}$

$10^{4}$

Exercise $\PageIndex{16}$

$17^{1}$

Answer

17

Exercise $\PageIndex{17}$

$\left(\frac{2}{9}\right)^{2}$

Exercise $\PageIndex{18}$

$(0.5)^{3}$

Answer

0.125

Exercise $\PageIndex{19}$

$(-2)^{6}$

Exercise $\PageIndex{20}$

$-2^{6}$

Answer

−64

Simplify Expressions Using the Product Property for Exponents

In the following exercises, simplify each expression.

Exercise $\PageIndex{21}$

$x^{4} \cdot x^{3}$

Exercise $\PageIndex{22}$

$p^{15} \cdot p^{16}$

Answer

$p^{31}$

Exercise $\PageIndex{23}$

$4^{10} \cdot 4^{6}$

Exercise $\PageIndex{24}$

8$\cdot 8^{5}$

Answer

$8^{6}$

Exercise $\PageIndex{25}$

$n \cdot n^{2} \cdot n^{4}$

Exercise $\PageIndex{26}$

$y^{c} \cdot y^{3}$

Answer

$y^{c+3}$

Simplify Expressions Using the Power Property for Exponents

In the following exercises, simplify each expression.

Exercise $\PageIndex{27}$

$\left(m^{3}\right)^{5}$

Exercise $\PageIndex{28}$

$\left(5^{3}\right)^{2}$

Answer

$5^{6}$

Exercise $\PageIndex{29}$

$\left(y^{4}\right)^{x}$

Exercise $\PageIndex{30}$

$\left(3^{r}\right)^{s}$

Answer

$3^{r s}$

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

Exercise $\PageIndex{31}$

$(4 a)^{2}$

Exercise $\PageIndex{32}$

$(-5 y)^{3}$

Answer

$-125 y^{3}$

Exercise $\PageIndex{33}$

$(2 m n)^{5}$

Exercise $\PageIndex{34}$

$(10 x y z)^{3}$

Answer

1000$x^{3} y^{3} z^{3}$

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

Exercise $\PageIndex{35}$

$\left(p^{2}\right)^{5} \cdot\left(p^{3}\right)^{6}$

Exercise $\PageIndex{36}$

$\left(4 a^{3} b^{2}\right)^{3}$

Answer

64$a^{9} b^{6}$

Exercise $\PageIndex{37}$

$(5 x)^{2}(7 x)$

Exercise $\PageIndex{38}$

$\left(2 q^{3}\right)^{4}(3 q)^{2}$

Answer

48$q^{14}$

Exercise $\PageIndex{39}$

$\left(\frac{1}{3} x^{2}\right)^{2}\left(\frac{1}{2} x\right)^{3}$

Exercise $\PageIndex{40}$

$\left(\frac{2}{5} m^{2} n\right)^{3}$

Answer

$\frac{8}{125} m^{6} n^{3}$

Multiply Monomials

In the following exercises 8, multiply the monomials.

Exercise $\PageIndex{41}$

$\left(-15 x^{2}\right)\left(6 x^{4}\right)$

Exercise $\PageIndex{42}$

$\left(-9 n^{7}\right)(-16 n)$

Answer

144$n^{8}$

Exercise $\PageIndex{43}$

$\left(7 p^{5} q^{3}\right)\left(8 p q^{9}\right)$

Exercise $\PageIndex{44}$

$\left(\frac{5}{9} a b^{2}\right)\left(27 a b^{3}\right)$

Answer

15$a^{2} b^{5}$

Multiply Polynomials

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

Exercise $\PageIndex{45}$

7(a+9)

Exercise $\PageIndex{46}$

−4(y+13)

Answer

−4y−52

Exercise $\PageIndex{47}$

−5(r−2)

Exercise $\PageIndex{48}$

p(p+3)

Answer

$p^{2}+3 p$

Exercise $\PageIndex{49}$

−m(m+15)

Exercise $\PageIndex{50}$

−6u(2u+7)

Answer

$-12 u^{2}-42 u$

Exercise $\PageIndex{51}$

9$\left(b^{2}+6 b+8\right)$

Exercise $\PageIndex{52}$

3$q^{2}\left(q^{2}-7 q+6\right) 3$

Answer

$3 q^{4}-21 q^{3}+18 q^{2}$

Exercise $\PageIndex{53}$

$(5 z-1) z$

Exercise $\PageIndex{54}$

$(b-4) \cdot 11$

Answer

11b−44

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using:

1. the Distributive Property,
2. the FOIL method,
3. the Vertical Method.

Exercise $\PageIndex{55}$

(x−4)(x+10)

Exercise $\PageIndex{56}$

(6y−7)(2y−5)

Answer

1. $12 y^{2}-44y+35$
2. $12 y^{2}-44y+35$
3. $12 y^{2}-44y+35$

In the following exercises, multiply the binomials. Use any method.

Exercise $\PageIndex{57}$

(x+3)(x+9)

Exercise $\PageIndex{58}$

(y−4)(y−8)

Answer

$y^{2}-12 y+32$

Exercise $\PageIndex{59}$

(p−7)(p+4)

Exercise $\PageIndex{60}$

(q+16)(q−3)

Answer

$q^{2}+13 q-48$

Exercise $\PageIndex{61}$

(5m−8)(12m+1)

Exercise $\PageIndex{62}$

$\left(u^{2}+6\right)\left(u^{2}-5\right)$

Answer

$u^{4}+u^{2}-30$

Exercise $\PageIndex{63}$

(9x−y)(6x−5)

Exercise $\PageIndex{64}$

(8mn+3)(2mn−1)

Answer

$16 m^{2} n^{2}-2 m n-3$

Multiply a Trinomial by a Binomial

In the following exercises, multiply using

1. the Distributive Property,
2. the Vertical Method.

Exercise $\PageIndex{65}$

$(n+1)\left(n^{2}+5 n-2\right)$

Exercise $\PageIndex{66}$

$(3 x-4)\left(6 x^{2}+x-10\right)$

Answer

1. $18 x^{3}-21 x^{2}-34 x+40$
2. $18 x^{3}-21 x^{2}-34 x+40$

In the following exercises, multiply. Use either method.

Exercise $\PageIndex{67}$

$(y-2)\left(y^{2}-8 y+9\right)$

Exercise $\PageIndex{68}$

$(7 m+1)\left(m^{2}-10 m-3\right)$

Answer

$7 m^{3}-69 m^{2}-31 m-3$

Special Products

Square a Binomial Using the Binomial Squares Pattern

In the following exercises, square each binomial using the Binomial Squares Pattern.

Exercise $\PageIndex{69}$

$(c+11)^{2}$

Exercise $\PageIndex{70}$

$(q-15)^{2}$

Answer

$q^{2}-30 q+225$

Exercise $\PageIndex{71}$

$\left(x+\frac{1}{3}\right)^{2}$

Exercise $\PageIndex{72}$

$(8 u+1)^{2}$

Answer

$64 u^{2}+16 u+1$

Exercise $\PageIndex{73}$

$\left(3 n^{3}-2\right)^{2}$

Exercise $\PageIndex{74}$

$(4 a-3 b)^{2}$

Answer

$16 a^{2}-24 a b+9 b^{2}$

Multiply Conjugates Using the Product of Conjugates Pattern

In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern.

Exercise $\PageIndex{75}$

(s−7)(s+7)

Exercise $\PageIndex{76}$

$\left(y+\frac{2}{5}\right)\left(y-\frac{2}{5}\right)$

Answer

$y^{2}-\frac{4}{25}$

Exercise $\PageIndex{77}$

$(12 c+13)(12 c-13)$

Exercise $\PageIndex{78}$

(6−r)(6+r)

Answer

$36-r^{2}$

Exercise $\PageIndex{79}$

$\left(u+\frac{3}{4} v\right)\left(u-\frac{3}{4} v\right)$

Exercise $\PageIndex{80}$

$\left(5 p^{4}-4 q^{3}\right)\left(5 p^{4}+4 q^{3}\right)$

Answer

$25 p^{8}-16 q^{6}$

Recognize and Use the Appropriate Special Product Pattern

In the following exercises, find each product.

Exercise $\PageIndex{81}$

$(3 m+10)^{2}$

Exercise $\PageIndex{82}$

(6a+11)(6a−11)

Answer

$36 a^{2}-121$

Exercise $\PageIndex{83}$

(5x+y)(x−5y)

Exercise $\PageIndex{84}$

$\left(c^{4}+9 d\right)^{2}$

Answer

$c^{8}+18 c^{4} d+81 d^{2}$

Exercise $\PageIndex{85}$

$\left(p^{5}+q^{5}\right)\left(p^{5}-q^{5}\right)$

Exercise $\PageIndex{86}$

$\left(a^{2}+4 b\right)\left(4 a-b^{2}\right)$

Answer

$4 a^{3}+3 a^{2} b-4 b^{3}$

Divide Monomials

Simplify Expressions Using the Quotient Property for Exponents

In the following exercises, simplify.

Exercise $\PageIndex{87}$

$\frac{u^{24}}{u^{6}}$

Exercise $\PageIndex{88}$

$\frac{10^{25}}{10^{5}}$

Answer

$10^{20}$

Exercise $\PageIndex{89}$

$\frac{3^{4}}{3^{6}}$

Exercise $\PageIndex{90}$

$\frac{v^{12}}{v^{48}}$

Answer

$\frac{1}{v^{36}}$

Exercise $\PageIndex{91}$

$\frac{x}{x^{5}}$

Exercise $\PageIndex{92}$

$\frac{5}{5^{8}}$

Answer

$\frac{1}{5^{7}}$

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

Exercise $\PageIndex{93}$

$75^{0}$

Exercise $\PageIndex{94}$

$x^{0}$

Answer

1

Exercise $\PageIndex{95}$

$-12^{0}$

Exercise $\PageIndex{96}$

$\left(-12^{0}\right)(-12)^{0}$

Answer

1

Exercise $\PageIndex{97}$

25$x^{0}$

Exercise $\PageIndex{98}$

$(25 x)^{0}$

Answer

1

Exercise $\PageIndex{99}$

$19 n^{0}-25 m^{0}$

Exercise $\PageIndex{100}$

$(19 n)^{0}-(25 m)^{0}$

Answer

0

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

Exercise $\PageIndex{101}$

$\left(\frac{2}{5}\right)^{3}$

Exercise $\PageIndex{102}$

$\left(\frac{m}{3}\right)^{4}$

Answer

$\frac{m^{4}}{81}$

Exercise $\PageIndex{103}$

$\left(\frac{r}{s}\right)^{8}$

Exercise $\PageIndex{104}$

$\left(\frac{x}{2 y}\right)^{6}$

Answer

$\frac{x^{6}}{64 y^{6}}$

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

Exercise $\PageIndex{105}$

$\frac{\left(x^{3}\right)^{5}}{x^{9}}$

Exercise $\PageIndex{106}$

$\frac{n^{10}}{\left(n^{5}\right)^{2}}$

Answer

1

Exercise $\PageIndex{107}$

$\left(\frac{q^{6}}{q^{8}}\right)^{3}$

Exercise $\PageIndex{108}$

$\left(\frac{r^{8}}{r^{3}}\right)^{4}$

Answer

$r^{20}$

Exercise $\PageIndex{109}$

$\left(\frac{c^{2}}{d^{5}}\right)^{9}$

Exercise $\PageIndex{110}$

$\left(\frac{3 x^{4}}{2 y^{2}}\right)^{5}$

Answer

$\frac{343 x^{20}}{32 y^{10}}$

Exercise $\PageIndex{111}$

$\left(\frac{v^{3} v^{9}}{v^{6}}\right)^{4}$

Exercise $\PageIndex{112}$

$\frac{\left(3 n^{2}\right)^{4}\left(-5 n^{4}\right)^{3}}{\left(-2 n^{5}\right)^{2}}$

Answer

$-\frac{10,125 n^{10}}{4}$

Divide Monomials

In the following exercises, divide the monomials.

Exercise $\PageIndex{113}$

$-65 y^{14} \div 5 y^{2}$

Exercise $\PageIndex{114}$

$\frac{64 a^{5} b^{9}}{-16 a^{10} b^{3}}$

Answer

$-\frac{4 b^{6}}{a^{5}}$

Exercise $\PageIndex{115}$

$\frac{144 x^{15} y^{8} z^{3}}{18 x^{10} y^{2} z^{12}}$

Exercise $\PageIndex{116}$

$\frac{\left(8 p^{6} q^{2}\right)\left(9 p^{3} q^{5}\right)}{16 p^{8} q^{7}}$

Answer

$\frac{9 p}{2}$

Divide Polynomials

Divide a Polynomial by a Monomial

In the following exercises, divide each polynomial by the monomial.

Exercise $\PageIndex{117}$

$\frac{42 z^{2}-18 z}{6}$

Exercise $\PageIndex{118}$

$\left(35 x^{2}-75 x\right) \div 5 x$

Answer

7x−15

Exercise $\PageIndex{119}$

$\frac{81 n^{4}+105 n^{2}}{-3}$

Exercise $\PageIndex{120}$

$\frac{550 p^{6}-300 p^{4}}{10 p^{3}}$

Answer

$55 p^{3}-30 p$

Exercise $\PageIndex{121}$

$\left(63 x y^{3}+56 x^{2} y^{4}\right) \div(7 x y)$

Exercise $\PageIndex{122}$

$\frac{96 a^{5} b^{2}-48 a^{4} b^{3}-56 a^{2} b^{4}}{8 a b^{2}}$

Answer

$12 a^{4}-6 a^{3} b-7 a b^{2}$

Exercise $\PageIndex{123}$

$\frac{57 m^{2}-12 m+1}{-3 m}$

Exercise $\PageIndex{124}$

$\frac{105 y^{5}+50 y^{3}-5 y}{5 y^{3}}$

Answer

$21 y^{2}+10-\frac{1}{y^{2}}$

Divide a Polynomial by a Binomial

In the following exercises, divide each polynomial by the binomial.

Exercise $\PageIndex{125}$

$\left(k^{2}-2 k-99\right) \div(k+9)$

Exercise $\PageIndex{126}$

$\left(v^{2}-16 v+64\right) \div(v-8)$

Answer

v−8

Exercise $\PageIndex{127}$

$\left(3 x^{2}-8 x-35\right) \div(x-5)$

Exercise $\PageIndex{128}$

$\left(n^{2}-3 n-14\right) \div(n+3)$

Answer

$n-6+\frac{4}{n+3}$

Exercise $\PageIndex{129}$

$\left(4 m^{3}+m-5\right) \div(m-1)$

Exercise $\PageIndex{130}$

$\left(u^{3}-8\right) \div(u-2)$

Answer

$u^{2}+2 u+4$

Integer Exponents and Scientific Notation

Use the Definition of a Negative Exponent

In the following exercises, simplify.

Exercise $\PageIndex{131}$

$9^{-2}$

Exercise $\PageIndex{132}$

$(-5)^{-3}$

Answer

$-\frac{1}{125}$

Exercise $\PageIndex{133}$

3$\cdot 4^{-3}$

Exercise $\PageIndex{134}$

$(6 u)^{-3}$

Answer

$\frac{1}{216 u^{3}}$

Exercise $\PageIndex{135}$

$\left(\frac{2}{5}\right)^{-1}$

Exercise $\PageIndex{136}$

$\left(\frac{3}{4}\right)^{-2}$

Answer

$\frac{16}{9}$

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

Exercise $\PageIndex{137}$

$p^{-2} \cdot p^{8}$

Exercise $\PageIndex{138}$

$q^{-6} \cdot q^{-5}$

Answer

$\frac{1}{q^{11}}$

Exercise $\PageIndex{139}$

$\left(c^{-2} d\right)\left(c^{-3} d^{-2}\right)$

Exercise $\PageIndex{140}$

$\left(y^{8}\right)^{-1}$

Answer

$\frac{1}{y^{8}}$

Exercise $\PageIndex{141}$

$\left(q^{-4}\right)^{-3}$

Exercise $\PageIndex{142}$

$\frac{a^{8}}{a^{12}}$

Answer

$\frac{1}{a^{4}}$

Exercise $\PageIndex{143}$

$\frac{n^{5}}{n^{-4}}$

Exercise $\PageIndex{144}$

$\frac{r^{-2}}{r^{-3}}$

Answer

r

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

Exercise $\PageIndex{145}$

8,500,000

Exercise $\PageIndex{146}$

0.00429

Answer

$4.29 \times 10^{-3}$

Exercise $\PageIndex{147}$

The thickness of a dime is about 0.053 inches.

Exercise $\PageIndex{148}$

In 2015, the population of the world was about 7,200,000,000 people.

Answer

$7.2 \times 10^{9}$

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

Exercise $\PageIndex{149}$

$3.8 \times 10^{5}$

Exercise $\PageIndex{150}$

$1.5 \times 10^{10}$

Answer

15,000,000,000

Exercise $\PageIndex{151}$

$9.1 \times 10^{-7}$

Exercise $\PageIndex{152}$

$5.5 \times 10^{-1}$

Answer

0.55

Multiply and Divide Using Scientific Notation

In the following exercises, multiply and write your answer in decimal form.

Exercise $\PageIndex{153}$

$\left(2 \times 10^{5}\right)\left(4 \times 10^{-3}\right)$

Exercise $\PageIndex{154}$

$\left(3.5 \times 10^{-2}\right)\left(6.2 \times 10^{-1}\right)$

Answer

0.0217

In the following exercises, divide and write your answer in decimal form.

Exercise $\PageIndex{155}$

$\frac{8 \times 10^{5}}{4 \times 10^{-1}}$

Exercise $\PageIndex{156}$

$\frac{9 \times 10^{-5}}{3 \times 10^{2}}$

Answer

0.0000003

Chapter Practice Test

Exercise $\PageIndex{1}$

For the polynomial $10 x^{4}+9 y^{2}-1$
ⓐ Is it a monomial, binomial, or trinomial?
ⓑ What is its degree?

In the following exercises, simplify each expression.

Exercise $\PageIndex{2}$

$\left(12 a^{2}-7 a+4\right)+\left(3 a^{2}+8 a-10\right)$

Answer

$15 a^{2}+a-6$

Exercise $\PageIndex{3}$

$\left(9 p^{2}-5 p+1\right)-\left(2 p^{2}-6\right)$

Exercise $\PageIndex{4}$

$\left(-\frac{2}{5}\right)^{3}$

Answer

$-\frac{8}{125}$

Exercise $\PageIndex{5}$

$u \cdot u^{4}$

Exercise $\PageIndex{6}$

$\left(4 a^{3} b^{5}\right)^{2}$

Answer

16$a^{6} b^{10}$

Exercise $\PageIndex{7}$

$\left(-9 r^{4} s^{5}\right)\left(4 r s^{7}\right)$

Exercise $\PageIndex{8}$

3$k\left(k^{2}-7 k+13\right)$

Answer

$3 k^{3}-21 k^{2}+39 k$

Exercise $\PageIndex{9}$

$(m+6)(m+12)$

Exercise $\PageIndex{10}$

(v−9)(9v−5)

Answer

$9 v^{2}-86 v+45$

Exercise $\PageIndex{11}$

(4c−11)(3c−8)

Exercise $\PageIndex{12}$

$(n-6)\left(n^{2}-5 n+4\right)$

Answer

$n^{3}-11 n^{2}+34 n-24$

Exercise $\PageIndex{13}$

$(2 x-15 y)(5 x+7 y)$

Exercise $\PageIndex{14}$

$(7 p-5)(7 p+5)$

Answer

$49 p^{2}-25$

Exercise $\PageIndex{15}$

$(9 v-2)^{2}$

Exercise $\PageIndex{16}$

$\frac{3^{8}}{3^{10}}$

Answer

$\frac{1}{9}$

Exercise $\PageIndex{17}$

$\left(\frac{m^{4} \cdot m}{m^{3}}\right)^{6}$

Exercise $\PageIndex{18}$

$\left(87 x^{15} y^{3} z^{22}\right)^{0}$

Answer

1

Exercise $\PageIndex{19}$

$\frac{80 c^{8} d^{2}}{16 c d^{10}}$

Exercise $\PageIndex{20}$

$\frac{12 x^{2}+42 x-6}{2 x}$

Answer

$6 x+21-\frac{3}{x}$

Exercise $\PageIndex{21}$

$\left(70 x y^{4}+95 x^{3} y\right) \div 5 x y$

Exercise $\PageIndex{22}$

$\frac{64 x^{3}-1}{4 x-1}$

Answer

$16 x^{2}+4 x+1$

Exercise $\PageIndex{23}$

$\left(y^{2}-5 y-18\right) \div(y+3)$

Exercise $\PageIndex{24}$

$5^{-2}$

Answer

$\frac{1}{25}$

Exercise $\PageIndex{25}$

$(4 m)^{-3}$

Exercise $\PageIndex{26}$

$q^{-4} \cdot q^{-5}$

Answer

$\frac{1}{q^{9}}$

Exercise $\PageIndex{27}$

$\frac{n^{-2}}{n^{-10}}$

Exercise $\PageIndex{28}$

Convert 83,000,000 to scientific notation.

Answer

$8.3 \times 10^{7}$

Exercise $\PageIndex{29}$

Convert $6.91 \times 10^{-5}$ to decimal form.

In the following exercises, simplify, and write your answer in decimal form.

Exercise $\PageIndex{30}$

$\left(3.4 \times 10^{9}\right)\left(2.2 \times 10^{-5}\right)$

Answer

74,800

Exercise $\PageIndex{31}$

$\frac{8.4 \times 10^{-3}}{4 \times 10^{3}}$

Exercise $\PageIndex{32}$

A helicopter flying at an altitude of 1000 feet drops a rescue package. The polynomial $-16 t^{2}+1000$ gives the height of the package t seconds a after it was dropped. Find the height when t=6 seconds.

Answer

424 feet