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Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

Chapter 2

Alyebraic Expressions - all with Video Answers

Educators


Section 1

Variables and Exponents

01:15

Problem 1

Write the given expression without exponents.
$$x^{6}$$

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01:05

Problem 2

Write the given expression without exponents.
$$y^{5}$$

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01:23

Problem 3

Write the given expression without exponents.
$$(-x)^{4}$$

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01:34

Problem 4

Write the given expression without exponents.
$$(-y)^{5}$$

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02:17

Problem 5

Write the given expression without exponents.
$$-x^{4}$$

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02:37

Problem 6

Write the given expression without exponents.
$$-y^{6}$$

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02:33

Problem 7

Write the given expression without exponents.
$$x^{2} y^{3}$$

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02:59

Problem 8

Write the given expression without exponents.
$$x^{4} y^{6}$$

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02:32

Problem 9

Write the given expression without exponents.
$$x^{2}+y^{3}$$

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03:17

Problem 10

Write the given expression without exponents.
$$x^{4}+y^{6}$$

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01:41

Problem 11

Write the given expression without exponents.
$$x y^{3}$$

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01:57

Problem 12

Write the given expression without exponents.
$$(x y)^{3}$$

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00:57

Problem 13

Write the given expression with exponents.
$$aaaa$$

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01:14

Problem 14

Write the given expression with exponents.
$$SSSSS$$

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02:45

Problem 15

Write the given expression with exponents.
$$x x y y y$$

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02:27

Problem 16

Write the given expression with exponents.
$$x x+y y y$$

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02:29

Problem 17

Write the given expression with exponents.
$$-r r s s s$$

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02:47

Problem 18

Write the given expression with exponents.
$$(-r)(-r) s s s$$

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03:42

Problem 19

Write the given expression with exponents.
$$-x x(-y)(-y)(-y)$$

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02:44

Problem 20

Write the given expression with exponents.
$$-x x-y y y$$

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02:34

Problem 21

Write the given expression with exponents.
$$(x x x)(x x x x x)$$

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03:14

Problem 22

Write the given expression with exponents.
$$(x x x)+(x x x x x)$$

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02:41

Problem 23

Evaluate the given expression.
$$3^{5}$$

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01:27

Problem 24

Evaluate the given expression.
$$5^{3}$$

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01:45

Problem 25

Evaluate the given expression.
$$-2^{3}$$

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01:40

Problem 26

Evaluate the given expression.
$$(-2)^{3}$$

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01:54

Problem 27

Evaluate the given expression.
$$(-2)^{4}$$

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02:11

Problem 28

Evaluate the given expression.
$$-2^{4}$$

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04:03

Problem 29

Evaluate the given expression.
$$3^{2}+3^{3}-3^{4}$$

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04:44

Problem 30

Evaluate the given expression.
$$4^{2}+4^{3}-4^{4}$$

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02:29

Problem 31

Evaluate the given expression.
$$4 \cdot 3^{2}-2 \cdot 5^{2}$$

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03:31

Problem 32

Evaluate the given expression.
$$7 \cdot 2^{3}-5 \cdot 3^{2}$$

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04:20

Problem 33

Evaluate the given expression.
$$(3-7)^{2}-(4-5)^{3}$$

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03:41

Problem 34

Evaluate the given expression.
$$(6-8)^{2}-(1-3)^{3}$$

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02:12

Problem 35

Evaluate the given expression.
$$3^{2} 4^{3}$$

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02:47

Problem 36

Evaluate the given expression.
$$2^{3} 2^{4}$$

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02:16

Problem 37

Evaluate the given expression.
$$3^{2} 3^{3}$$

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02:09

Problem 38

Evaluate the given expression.
$$2^{3} 3^{4}$$

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02:38

Problem 39

Simplify the given expression as completely as possible.
$$x^{3} x^{8}$$

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01:54

Problem 40

Simplify the given expression as completely as possible.
$$y^{4} y^{6}$$

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01:52

Problem 41

Simplify the given expression as completely as possible.
$$a^{2} a^{7}$$

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02:35

Problem 42

Simplify the given expression as completely as possible.
$$t^{5} t^{9}$$

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02:09

Problem 43

Simplify the given expression as completely as possible.
$$c^{4} c^{3} c^{2}$$

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02:38

Problem 44

Simplify the given expression as completely as possible.
$$m^{5} m^{4} m^{6}$$

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02:27

Problem 45

Simplify the given expression as completely as possible.
$$\left(a^{3}\right)^{2}$$

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01:44

Problem 46

Simplify the given expression as completely as possible.
$$a^{3} a^{2}$$

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02:15

Problem 47

Simplify the given expression as completely as possible.
$$t^{5} t^{2}$$

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01:42

Problem 48

Simplify the given expression as completely as possible.
$$\left(t^{5}\right)^{2}$$

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01:44

Problem 49

Simplify the given expression as completely as possible.
$$x^{3} x^{5}$$

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01:37

Problem 50

Simplify the given expression as completely as possible.
$$y^{4} y^{6}$$

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02:02

Problem 51

Simplify the given expression as completely as possible.
$$a a^{2} a^{4}$$

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02:12

Problem 52

Simplify the given expression as completely as possible.
$$m^{3} m m^{5}$$

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02:07

Problem 53

Simplify the given expression as completely as possible.
$$(3 x)(5 x)(4 x)$$

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02:06

Problem 54

Simplify the given expression as completely as possible.
$$(2 a)(3 a)(6 a)$$

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02:24

Problem 55

Simplify the given expression as completely as possible.
$$\left(3 r^{2}\right)\left(2 r^{3}\right)$$

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02:26

Problem 56

Simplify the given expression as completely as possible.
$$\left(4 w^{5}\right)\left(5 w^{4}\right)$$

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02:38

Problem 57

Simplify the given expression as completely as possible.
$$\left(-3 x^{3}\right)\left(5 x^{2}\right)$$

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02:36

Problem 58

Simplify the given expression as completely as possible.
$$(-4 x)\left(6 x^{5}\right)$$

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03:31

Problem 59

Simplify the given expression as completely as possible.
$$\left(-c^{4}\right)\left(2^{3}\right)(-5 c)$$

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02:56

Problem 60

Simplify the given expression as completely as possible.
$$(-3 p)\left(-2 p^{5}\right)\left(p^{2}\right)$$

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02:44

Problem 61

Simplify the given expression as completely as possible.
$$\left(8 x^{3} y^{2}\right)\left(4 x y^{5}\right)$$

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02:47

Problem 62

Simplify the given expression as completely as possible.
$$\left(7 x^{2} y^{3}\right)\left(5 x y^{4}\right)$$

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02:41

Problem 63

Simplify the given expression as completely as possible.
$$(-2 x y)\left(x^{2} y^{2}\right)(-3 x y)$$

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03:11

Problem 64

Simplify the given expression as completely as possible.
$$(-8 x)\left(-3 x y^{2}\right)\left(5 x^{3} y^{2}\right)$$

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01:55

Problem 65

Simplify the given expression as completely as possible.
$$\left(3 a^{4}\right)^{2}$$

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01:41

Problem 66

Simplify the given expression as completely as possible.
$$\left(4 a^{3}\right)^{2}$$

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01:34

Problem 67

Simplify the given expression as completely as possible.
$$\left(-4 n^{2}\right)^{3}$$

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02:00

Problem 68

Simplify the given expression as completely as possible.
$$\left(-5 n^{4}\right)^{3}$$

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02:00

Problem 69

Simplify the given expression as completely as possible.
$$\left(x^{2}\right)^{3}\left(x^{4}\right)^{2}$$

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02:00

Problem 70

Simplify the given expression as completely as possible.
$$\left(x^{3}\right)^{2}\left(x^{2}\right)^{4}$$

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02:08

Problem 71

Evaluate each expression. Round off your answer to the nearest thousandth where necessary.
$$(0.52)^{4}$$

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01:57

Problem 72

Evaluate each expression. Round off your answer to the nearest thousandth where necessary.
$$(1.83)^{5}$$

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01:54

Problem 73

Evaluate each expression. Round off your answer to the nearest thousandth where necessary.
$$(1.4)^{8}$$

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01:59

Problem 74

Evaluate each expression. Round off your answer to the nearest thousandth where necessary.
$$(-2.7)^{9}$$

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01:25

Problem 75

Evaluate each expression. Round off your answer to the nearest thousandth where necessary.
$$5.1(4.6)^{2}$$

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01:42

Problem 76

Evaluate each expression. Round off your answer to the nearest thousandth where necessary.
$$2.3(7.1)^{3}$$

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01:49

Problem 77

Evaluate each expression. Round off your answer to the nearest thousandth where necessary.
$$(3.81)^{3}-(2.64)^{2}$$

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01:28

Problem 78

Evaluate each expression. Round off your answer to the nearest thousandth where necessary.
$$(-5.4)^{2}-(4.1)^{2}$$

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02:29

Problem 79

State in words the difference between $3 \cdot 2^{4}$ and $(3 \cdot 2)^{4}$

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12:07

Problem 80

Explain what is wrong with each of the following:
(a) $3 \cdot 2^{2} \stackrel{?}{=} 6^{2} \stackrel{?}{=} 36$
(b) $3 x^{4} \stackrel{?}{=} 3 x \cdot 3 x \cdot 3 x \cdot 3 x$
(c) $5^{4} \cdot 2 \stackrel{?}{=} 20 \cdot 2 \stackrel{?}{=}40$
(d) $\left(3 x^{3}\right)^{2} \stackrel{?}{=} 6 x^{6}$
(e) $-3^{4} \stackrel{?}{=}(-3) \cdot(-3) \cdot(-3)(-3) \stackrel{?}{=} 81$
(f) $x^{4}+x^{5} \stackrel{?}{=} x^{9}$
(g) $x^{2} \cdot x^{7} \stackrel{?}{=} x^{14}$
(h) $\left(x^{2}\right)^{4} \stackrel{?}{=} x^{6}$

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01:38

Problem 81

Compare and contrast the expressions $3 \cdot 5$ and $5^{3}$.

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01:45

Problem 82

Compare and contrast the expressions $3^{5}$ and $5^{3}$.

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01:39

Problem 83

Compare and contrast the expressions $2^{4}$ and $4^{2} .$ Does the fact that both of these expressions have a numerical value of 16 affect your answer?

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