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# Chapter 6 Review Exercises

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## Chapter 6 Review Exercises

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. $$7 y^{3}+y^{2}-2 y-4$$
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
1. 3
2. 4
3. 2
4. 4
5. 0

In the following exercises, add or subtract the monomials.

##### Exercise $$\PageIndex{5}$$

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

##### Exercise $$\PageIndex{6}$$

$$-14 k+19 k$$

5k

12q−(−6q)

−9c−18c

−27c

12x−4y−9x

##### Exercise $$\PageIndex{2}$$

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

7$$n^{2}$$

##### Exercise $$\PageIndex{3}$$

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

##### Exercise $$\PageIndex{4}$$

13a+b

13a+b

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 $$\PageIndex{6}$$

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

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

##### Exercise $$\PageIndex{7}$$

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

##### Exercise $$\PageIndex{8}$$

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

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

##### 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 $$\left(5 a^{3}-7\right)$$

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

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
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.

12,000

### Use Multiplication Properties of Exponents

Simplify Expressions with Exponents

In the following exercises, simplify.

##### Exercise $$\PageIndex{15}$$

$$10^{4}$$

##### Exercise $$\PageIndex{16}$$

$$17^{1}$$

17

##### Exercise $$\PageIndex{17}$$

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

##### Exercise $$\PageIndex{18}$$

$$(0.5)^{3}$$

0.125

##### Exercise $$\PageIndex{19}$$

$$(-2)^{6}$$

##### Exercise $$\PageIndex{20}$$

$$-2^{6}$$

−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 $$\PageIndex{22}$$

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

$$p^{31}$$

##### Exercise $$\PageIndex{23}$$

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

##### Exercise $$\PageIndex{24}$$

8$$\cdot 8^{5}$$

$$8^{6}$$

##### Exercise $$\PageIndex{25}$$

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

##### Exercise $$\PageIndex{26}$$

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

$$y^{c+3}$$

Simplify Expressions Using the Power Property for Exponents

In the following exercises, simplify each expression.

##### Exercise $$\PageIndex{27}$$

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

##### Exercise $$\PageIndex{28}$$

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

$$5^{6}$$

##### Exercise $$\PageIndex{29}$$

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

##### Exercise $$\PageIndex{30}$$

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

$$3^{r s}$$

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

##### Exercise $$\PageIndex{31}$$

$$(4 a)^{2}$$

##### Exercise $$\PageIndex{32}$$

$$(-5 y)^{3}$$

$$-125 y^{3}$$

##### Exercise $$\PageIndex{33}$$

$$(2 m n)^{5}$$

##### Exercise $$\PageIndex{34}$$

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

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 $$\PageIndex{36}$$

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

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

##### Exercise $$\PageIndex{37}$$

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

##### Exercise $$\PageIndex{38}$$

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

48$$q^{14}$$

##### Exercise $$\PageIndex{39}$$

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

##### Exercise $$\PageIndex{40}$$

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

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

Multiply Monomials

In the following exercises 8, multiply the monomials.

##### Exercise $$\PageIndex{41}$$

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

##### Exercise $$\PageIndex{42}$$

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

144$$n^{8}$$

##### Exercise $$\PageIndex{43}$$

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

##### Exercise $$\PageIndex{44}$$

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

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

### Multiply Polynomials

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

7(a+9)

−4(y+13)

−4y−52

−5(r−2)

##### Exercise $$\PageIndex{48}$$

p(p+3)

$$p^{2}+3 p$$

−m(m+15)

##### Exercise $$\PageIndex{50}$$

−6u(2u+7)

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

##### Exercise $$\PageIndex{51}$$

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

##### Exercise $$\PageIndex{52}$$

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

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

##### Exercise $$\PageIndex{53}$$

$$(5 z-1) z$$

##### Exercise $$\PageIndex{54}$$

$$(b-4) \cdot 11$$

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.

(x−4)(x+10)

##### Exercise $$\PageIndex{56}$$

(6y−7)(2y−5)

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.

(x+3)(x+9)

##### Exercise $$\PageIndex{58}$$

(y−4)(y−8)

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

(p−7)(p+4)

##### Exercise $$\PageIndex{60}$$

(q+16)(q−3)

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

(5m−8)(12m+1)

##### Exercise $$\PageIndex{62}$$

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

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

(9x−y)(6x−5)

##### Exercise $$\PageIndex{64}$$

(8mn+3)(2mn−1)

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

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 $$\PageIndex{66}$$

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

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 $$\PageIndex{68}$$

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

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

### 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 $$\PageIndex{70}$$

$$(q-15)^{2}$$

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

##### Exercise $$\PageIndex{71}$$

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

##### Exercise $$\PageIndex{72}$$

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

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

##### Exercise $$\PageIndex{73}$$

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

##### Exercise $$\PageIndex{74}$$

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

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

Multiply Conjugates Using the Product of Conjugates Pattern

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

(s−7)(s+7)

##### Exercise $$\PageIndex{76}$$

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

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

##### Exercise $$\PageIndex{77}$$

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

##### Exercise $$\PageIndex{78}$$

(6−r)(6+r)

$$36-r^{2}$$

##### Exercise $$\PageIndex{79}$$

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

##### Exercise $$\PageIndex{80}$$

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

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

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)

$$36 a^{2}-121$$

(5x+y)(x−5y)

##### Exercise $$\PageIndex{84}$$

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

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

##### Exercise $$\PageIndex{85}$$

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

##### Exercise $$\PageIndex{86}$$

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

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

### Divide Monomials

Simplify Expressions Using the Quotient Property for Exponents

In the following exercises, simplify.

##### Exercise $$\PageIndex{87}$$

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

##### Exercise $$\PageIndex{88}$$

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

$$10^{20}$$

##### Exercise $$\PageIndex{89}$$

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

##### Exercise $$\PageIndex{90}$$

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

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

##### Exercise $$\PageIndex{91}$$

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

##### Exercise $$\PageIndex{92}$$

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

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

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

##### Exercise $$\PageIndex{93}$$

$$75^{0}$$

##### Exercise $$\PageIndex{94}$$

$$x^{0}$$

1

##### Exercise $$\PageIndex{95}$$

$$-12^{0}$$

##### Exercise $$\PageIndex{96}$$

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

1

##### Exercise $$\PageIndex{97}$$

25$$x^{0}$$

##### Exercise $$\PageIndex{98}$$

$$(25 x)^{0}$$

1

##### Exercise $$\PageIndex{99}$$

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

##### Exercise $$\PageIndex{100}$$

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

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 $$\PageIndex{102}$$

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

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

##### Exercise $$\PageIndex{103}$$

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

##### Exercise $$\PageIndex{104}$$

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

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

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

##### Exercise $$\PageIndex{105}$$

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

##### Exercise $$\PageIndex{106}$$

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

1

##### Exercise $$\PageIndex{107}$$

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

##### Exercise $$\PageIndex{108}$$

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

$$r^{20}$$

##### Exercise $$\PageIndex{109}$$

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

##### Exercise $$\PageIndex{110}$$

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

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

##### Exercise $$\PageIndex{111}$$

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

##### Exercise $$\PageIndex{112}$$

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

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

Divide Monomials

In the following exercises, divide the monomials.

##### Exercise $$\PageIndex{113}$$

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

##### Exercise $$\PageIndex{114}$$

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

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

##### Exercise $$\PageIndex{115}$$

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

##### Exercise $$\PageIndex{116}$$

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

$$\frac{9 p}{2}$$

### 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 $$\PageIndex{118}$$

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

7x−15

##### Exercise $$\PageIndex{119}$$

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

##### Exercise $$\PageIndex{120}$$

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

$$55 p^{3}-30 p$$

##### Exercise $$\PageIndex{121}$$

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

##### Exercise $$\PageIndex{122}$$

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

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

##### Exercise $$\PageIndex{123}$$

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

##### Exercise $$\PageIndex{124}$$

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

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

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 $$\PageIndex{126}$$

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

v−8

##### Exercise $$\PageIndex{127}$$

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

##### Exercise $$\PageIndex{128}$$

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

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

##### Exercise $$\PageIndex{129}$$

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

##### Exercise $$\PageIndex{130}$$

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

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

### Integer Exponents and Scientific Notation

Use the Definition of a Negative Exponent

In the following exercises, simplify.

##### Exercise $$\PageIndex{131}$$

$$9^{-2}$$

##### Exercise $$\PageIndex{132}$$

$$(-5)^{-3}$$

$$-\frac{1}{125}$$

##### Exercise $$\PageIndex{133}$$

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

##### Exercise $$\PageIndex{134}$$

$$(6 u)^{-3}$$

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

##### Exercise $$\PageIndex{135}$$

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

##### Exercise $$\PageIndex{136}$$

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

$$\frac{16}{9}$$

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

##### Exercise $$\PageIndex{137}$$

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

##### Exercise $$\PageIndex{138}$$

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

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

##### Exercise $$\PageIndex{139}$$

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

##### Exercise $$\PageIndex{140}$$

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

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

##### Exercise $$\PageIndex{141}$$

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

##### Exercise $$\PageIndex{142}$$

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

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

##### Exercise $$\PageIndex{143}$$

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

##### Exercise $$\PageIndex{144}$$

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

r

Convert from Decimal Notation to Scientific Notation

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

8,500,000

##### Exercise $$\PageIndex{146}$$

0.00429

$$4.29 \times 10^{-3}$$

##### 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.

$$7.2 \times 10^{9}$$

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 $$\PageIndex{150}$$

$$1.5 \times 10^{10}$$

15,000,000,000

##### Exercise $$\PageIndex{151}$$

$$9.1 \times 10^{-7}$$

##### Exercise $$\PageIndex{152}$$

$$5.5 \times 10^{-1}$$

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 $$\PageIndex{154}$$

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

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 $$\PageIndex{156}$$

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

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 $$\PageIndex{2}$$

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

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

##### Exercise $$\PageIndex{3}$$

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

##### Exercise $$\PageIndex{4}$$

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

$$-\frac{8}{125}$$

##### Exercise $$\PageIndex{5}$$

$$u \cdot u^{4}$$

##### Exercise $$\PageIndex{6}$$

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

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

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

##### Exercise $$\PageIndex{9}$$

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

##### Exercise $$\PageIndex{10}$$

(v−9)(9v−5)

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

(4c−11)(3c−8)

##### Exercise $$\PageIndex{12}$$

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

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

##### Exercise $$\PageIndex{13}$$

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

##### Exercise $$\PageIndex{14}$$

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

$$49 p^{2}-25$$

##### Exercise $$\PageIndex{15}$$

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

##### Exercise $$\PageIndex{16}$$

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

$$\frac{1}{9}$$

##### Exercise $$\PageIndex{17}$$

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

##### Exercise $$\PageIndex{18}$$

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

1

##### Exercise $$\PageIndex{19}$$

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

##### Exercise $$\PageIndex{20}$$

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

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

##### Exercise $$\PageIndex{21}$$

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

##### Exercise $$\PageIndex{22}$$

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

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

##### Exercise $$\PageIndex{23}$$

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

##### Exercise $$\PageIndex{24}$$

$$5^{-2}$$

$$\frac{1}{25}$$

##### Exercise $$\PageIndex{25}$$

$$(4 m)^{-3}$$

##### Exercise $$\PageIndex{26}$$

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

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

##### Exercise $$\PageIndex{27}$$

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

##### Exercise $$\PageIndex{28}$$

Convert 83,000,000 to scientific notation.

$$8.3 \times 10^{7}$$

##### 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 $$\PageIndex{30}$$

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

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.