Algebra A Combined Function

Problem 1

Evaluate each expression.
$$
7^{2}
$$

Julie Silva

Numerade Educator

Problem 2

Evaluate each expression.
$$
-3^{2}
$$

James Kiss

Numerade Educator

Problem 3

Evaluate each expression.
$$
(-5)^{1}
$$

Erika Bustos

Numerade Educator

Problem 4

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

James Kiss

Numerade Educator

Problem 5

Evaluate each expression.
$$
-2^{4}
$$

Julie Silva

Numerade Educator

Problem 6

Evaluate each expression.
$$
-4^{3}
$$

Amy Jiang

Numerade Educator

Problem 7

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

Julie Silva

Numerade Educator

Problem 8

Evaluate each expression.
$$
(-4)^{3}
$$

Amy Jiang

Numerade Educator

Problem 9

Evaluate each expression.
$$
\left(\frac{1}{3}\right)^{3}
$$

Amy Jiang

Numerade Educator

Problem 10

Evaluate each expression.
$$
\left(-\frac{1}{9}\right)^{2}
$$

Erika Bustos

Numerade Educator

Problem 11

Evaluate each expression.
$$
7 \cdot 2^{4}
$$

Erika Bustos

Numerade Educator

00:08

Problem 12

Evaluate each expression.
$$
9 \cdot 2^{2}
$$

Erika Bustos

Numerade Educator

Problem 13

Evaluate each expression with the given replacement values.
$$
x^{2} \text { when } x=-2
$$

Erika Bustos

Numerade Educator

00:24

Problem 14

Evaluate each expression with the given replacement values.
$$
x^{3} \text { when } x=-2
$$

Erika Bustos

Numerade Educator

Problem 15

Evaluate each expression with the given replacement values.
$$
5 x^{3} \text { when } x=3
$$

Erika Bustos

Numerade Educator

Problem 16

Evaluate each expression with the given replacement values.
$$
4 x^{2} \text { when } x=5
$$

Erika Bustos

Numerade Educator

00:26

Problem 17

Evaluate each expression with the given replacement values.
$$
2 x y^{2} \text { when } x=3 \text { and } y=-5
$$

Erika Bustos

Numerade Educator

00:29

Problem 18

Evaluate each expression with the given replacement values.
$$
-4 x^{2} y^{3} \text { when } x=2 \text { and } y=-1
$$

Erika Bustos

Numerade Educator

00:31

Problem 19

Evaluate each expression with the given replacement values.
$$
\frac{2 z^{4}}{5} \text { when } z=-2
$$

Erika Bustos

Numerade Educator

00:31

Problem 20

Evaluate each expression with the given replacement values.
$$
\frac{10}{3 y^{3}} \text { when } y=-3
$$

Erika Bustos

Numerade Educator

Problem 21

Use the product rule to simplify each expression.
$$
x^{2} \cdot x^{5}
$$

Erika Bustos

Numerade Educator

00:13

Problem 22

Use the product rule to simplify each expression.
$$
y^{2} \cdot y
$$

Erika Bustos

Numerade Educator

Problem 23

Use the product rule to simplify each expression.
$$
(-3)^{3} \cdot(-3)^{9}
$$

Erika Bustos

Numerade Educator

Problem 24

Use the product rule to simplify each expression.
$$
(-5)^{7} \cdot(-5)^{6}
$$

Erika Bustos

Numerade Educator

Problem 25

Use the product rule to simplify each expression.
$$
\left(5 y^{4}\right)(3 y)
$$

Erika Bustos

Numerade Educator

Problem 26

Use the product rule to simplify each expression.
$$
\left(-2 z^{3}\right)\left(-2 z^{2}\right)
$$

Erika Bustos

Numerade Educator

00:26

Problem 27

Use the product rule to simplify each expression.
$$
\left(x^{9} y\right)\left(x^{10} y^{5}\right)
$$

Erika Bustos

Numerade Educator

00:18

Problem 28

Use the product rule to simplify each expression.
$$
\left(a^{2} b\right)\left(a^{13} b^{17}\right)
$$

Erika Bustos

Numerade Educator

Problem 29

Use the product rule to simplify each expression.
$$
\left(-8 m n^{6}\right)\left(9 m^{2} n^{2}\right)
$$

Erika Bustos

Numerade Educator

Problem 30

Use the product rule to simplify each expression.
$$
\left(-7 a^{3} b^{3}\right)\left(7 a^{19} b\right)
$$

Erika Bustos

Numerade Educator

Problem 31

Use the product rule to simplify each expression.
$$
\left(4 z^{10}\right)\left(-6 z^{7}\right)\left(z^{3}\right)
$$

Erika Bustos

Numerade Educator

00:24

Problem 32

Use the product rule to simplify each expression.
$$
\left(12 x^{5}\right)\left(-x^{6}\right)\left(x^{4}\right)
$$

Erika Bustos

Numerade Educator

Problem 33

The rectangle below has width $4 x^{2}$ feet and length $5 x^{3}$ feet. Find its area as an expression in $x$.

Erika Bustos

Numerade Educator

Problem 34

The parallelogram below has base length $9 y^{7}$ meters and height $2 y^{10}$ meters. Find its area as an expression in $y$.

Erika Bustos

Numerade Educator

00:18

Problem 35

Use the power rule and the power of a product or quotient rule to simplify eachexpression.
$$
\left(x^{9}\right)^{4}
$$

Erika Bustos

Numerade Educator

Problem 36

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(y^{7}\right)^{5}
$$

Erika Bustos

Numerade Educator

Problem 37

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
(p q)^{8}
$$

Erika Bustos

Numerade Educator

Problem 38

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
(a b)^{6}
$$

Erika Bustos

Numerade Educator

Problem 39

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(2 a^{5}\right)^{3}
$$

Erika Bustos

Numerade Educator

Problem 40

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(4 x^{6}\right)^{2}
$$

Erika Bustos

Numerade Educator

Problem 41

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(x^{2} y^{3}\right)^{5}
$$

Erika Bustos

Numerade Educator

Problem 42

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(a^{4} b\right)^{7}
$$

Erika Bustos

Numerade Educator

00:50

Problem 43

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(-7 a^{2} b^{5} c\right)^{2}
$$

Erika Bustos

Numerade Educator

00:49

Problem 44

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(-3 x^{7} y z^{2}\right)^{3}
$$

Erika Bustos

Numerade Educator

Problem 45

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(\frac{r}{s}\right)^{9}
$$

Erika Bustos

Numerade Educator

00:20

Problem 46

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(\frac{q}{t}\right)^{11}
$$

Erika Bustos

Numerade Educator

00:39

Problem 47

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(\frac{m p}{n}\right)^{9}
$$

Erika Bustos

Numerade Educator

00:36

Problem 48

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(\frac{x y}{7}\right)^{2}
$$

Erika Bustos

Numerade Educator

01:02

Problem 49

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(\frac{-2 x z}{y^{5}}\right)^{2}
$$

Erika Bustos

Numerade Educator

01:16

Problem 50

Use the power rule and the power of a product or quotient rule to simplify each expression.
$$
\left(\frac{x y^{4}}{-3 z^{3}}\right)^{3}
$$

Erika Bustos

Numerade Educator

Problem 51

The square shown has sides of length $8 z^{5}$ decimeters. Find its area.

Erika Bustos

Numerade Educator

00:35

Problem 52

Given the circle below with radius $5 y$ centimeters, find its area. Do not approximate $\pi$.

Erika Bustos

Numerade Educator

00:39

Problem 53

The vault below is in the shape of a cube. If each side is $3 y^{4}$ feet, find its volume.

Erika Bustos

Numerade Educator

00:59

Problem 54

The silo shown is in the shape of a cylinder. If its radius is $4 x$ meters and its height is $5 x^{3}$ meters, find its volume. Do not approximate $\pi$.

Erika Bustos

Numerade Educator

Problem 55

Use the quotient rule and simplify each expression.
$$
\frac{x^{3}}{x}
$$

Erika Bustos

Numerade Educator

Problem 56

Use the quotient rule and simplify each expression.
$$
\frac{y^{10}}{y^{9}}
$$

Erika Bustos

Numerade Educator

00:34

Problem 57

Use the quotient rule and simplify each expression.
$$
\frac{(-4)^{6}}{(-4)^{3}}
$$

Erika Bustos

Numerade Educator

00:28

Problem 58

Use the quotient rule and simplify each expression.
$$
\frac{(-6)^{13}}{(-6)^{11}}
$$

Erika Bustos

Numerade Educator

Problem 59

Use the quotient rule and simplify each expression.
$$
\frac{p^{7} q^{20}}{p q^{15}}
$$

Erika Bustos

Numerade Educator

00:24

Problem 60

Use the quotient rule and simplify each expression.
$$
\frac{x^{8} y^{6}}{x y^{5}}
$$

Erika Bustos

Numerade Educator

00:43

Problem 61

Use the quotient rule and simplify each expression.
$$
\frac{7 x^{2} y^{6}}{14 x^{2} y^{3}}
$$

Erika Bustos

Numerade Educator

00:27

Problem 62

Use the quotient rule and simplify each expression.
$$
\frac{9 a^{4} b^{7}}{27 a b^{2}}
$$

Erika Bustos

Numerade Educator

Problem 63

Simplify each expression.
$$
7^{0}
$$

Shaza Hammoud

Numerade Educator

00:07

Problem 64

Simplify each expression.
$$
23^{0}
$$

Erika Bustos

Numerade Educator

00:30

Problem 65

Simplify each expression.
$$
(2 x)^{0}
$$

Shaza Hammoud

Numerade Educator

Problem 66

Simplify each expression.
$$
(4 y)^{0}
$$

Erika Bustos

Numerade Educator

Problem 67

Simplify each expression.
$$
-7 x^{0}
$$

Erika Bustos

Numerade Educator

00:30

Problem 68

Simplify each expression.
$$
-2 x^{0}
$$

Shaza Hammoud

Numerade Educator

Problem 69

Simplify each expression.
$$
5^{0}+y^{0}
$$

Erika Bustos

Numerade Educator

Problem 70

Simplify each expression.
$$
-3^{0}+4^{0}
$$

Erika Bustos

Numerade Educator

Problem 72

Simplify each expression.
$$
(-9)^{2}
$$

Erika Bustos

Numerade Educator

Problem 73

Simplify each expression.
$$
\left(\frac{1}{4}\right)^{3}
$$

Erika Bustos

Numerade Educator

01:11

Problem 74

Simplify each expression.
$$
\left(\frac{2}{3}\right)^{3}
$$

Kevin Corkran-Itagaki

Numerade Educator

00:08

Problem 75

Simplify each expression.
$$
b^{4} b^{2}
$$

Erika Bustos

Numerade Educator

Problem 76

Simplify each expression.
$$
y^{4} y
$$

Erika Bustos

Numerade Educator

01:05

Problem 77

Simplify each expression.
$$
a^{2} a^{3} a^{4}
$$

Jeffrey Morris

Numerade Educator

Problem 78

Simplify each expression.
$$
x^{2} x^{15} x^{9}
$$

Erika Bustos

Numerade Educator

Problem 79

Simplify each expression.
$$
\left(2 x^{3}\right)\left(-8 x^{4}\right)
$$

Erika Bustos

Numerade Educator

Problem 80

Simplify each expression.
$$
\left(3 y^{4}\right)(-5 y)
$$

Erika Bustos

Numerade Educator

Problem 81

Simplify each expression.
$$
\left(a^{7} b^{12}\right)\left(a^{4} b^{8}\right)
$$

Erika Bustos

Numerade Educator

00:13

Problem 82

Simplify each expression.
$$
\left(y^{2} z^{2}\right)\left(y^{15} z^{13}\right)
$$

Erika Bustos

Numerade Educator

Problem 83

Simplify each expression.
$$
\left(-2 m n^{6}\right)\left(-13 m^{8} n\right)
$$

Erika Bustos

Numerade Educator

00:20

Problem 84

Simplify each expression.
$$
\left(-3 s^{5} t\right)\left(-7 s t^{10}\right)
$$

Erika Bustos

Numerade Educator

Problem 85

Simplify each expression.
$$
\left(z^{4}\right)^{10}
$$

Erika Bustos

Numerade Educator

Problem 86

Simplify each expression.
$$
\left(t^{5}\right)^{11}
$$

Erika Bustos

Numerade Educator

00:34

Problem 87

Simplify each expression.
$$
(4 a b)^{3}
$$

Erika Bustos

Numerade Educator

00:36

Problem 88

Simplify each expression.
$$
(2 a b)^{4}
$$

Erika Bustos

Numerade Educator

Problem 89

Simplify each expression.
$$
\left(-6 x y z^{3}\right)^{2}
$$

Erika Bustos

Numerade Educator

01:00

Problem 90

Simplify each expression.
$$
\left(-3 x y^{2} a^{3}\right)^{3}
$$

Erika Bustos

Numerade Educator

Problem 91

Simplify each expression.
$$
\frac{3 x^{5}}{x^{4}}
$$

Erika Bustos

Numerade Educator

Problem 92

Simplify each expression.
$$
\frac{5 x^{9}}{x^{3}}
$$

Erika Bustos

Numerade Educator

00:30

Problem 93

Simplify each expression.
$$
(9 x y)^{2}
$$

Erika Bustos

Numerade Educator

Problem 94

Simplify each expression.
$$
(2 a b)^{5}
$$

Erika Bustos

Numerade Educator

Problem 95

Simplify each expression.
$$
2^{3}+2^{0}
$$

Erika Bustos

Numerade Educator

Problem 96

Simplify each expression.
$$
7^{2}-7^{0}
$$

Erika Bustos

Numerade Educator

00:52

Problem 97

Simplify each expression.
$$
\left(\frac{3 y^{5}}{6 x^{4}}\right)^{3}
$$

Erika Bustos

Numerade Educator

01:12

Problem 98

Simplify each expression.
$$
\left(\frac{2 a b}{6 y z}\right)^{4}
$$

Erika Bustos

Numerade Educator

Problem 99

Simplify each expression.
$$
\frac{2 x^{3} y^{2} z}{x y z}
$$

Erika Bustos

Numerade Educator

Problem 100

Simplify each expression.
$$
\frac{x^{12} y^{13}}{x^{5} y^{7}}
$$

Erika Bustos

Numerade Educator

00:20

Problem 101

Simplify each expression.
$$
\left(5^{0}\right)^{3}+\left(y^{0}\right)^{7}
$$

Erika Bustos

Numerade Educator

Problem 102

Simplify each expression.
$$
\left(9^{0}\right)^{4}+\left(z^{0}\right)^{5}
$$

Erika Bustos

Numerade Educator

00:57

Problem 103

Simplify each expression.
$$
\left(\frac{5 x^{9}}{10 y^{11}}\right)^{2}
$$

Erika Bustos

Numerade Educator

00:59

Problem 104

Simplify each expression.
$$
\left(\frac{3 a^{4}}{9 b^{5}}\right)^{2}
$$

Erika Bustos

Numerade Educator

01:29

Problem 105

Simplify each expression.
$$
\frac{\left(2 a^{5} b^{3}\right)^{4}}{-16 a^{20} b^{7}}
$$

Erika Bustos

Numerade Educator

01:22

Problem 106

Simplify each expression.
$$
\frac{\left(2 x^{6} y^{2}\right)^{5}}{-32 x^{20} y^{10}}
$$

Erika Bustos

Numerade Educator

00:04

Problem 107

Subtract.
$$
5-7
$$

Erika Bustos

Numerade Educator

00:05

Problem 108

Subtract.
$$
9-12
$$

Erika Bustos

Numerade Educator

00:04

Problem 109

Subtract.
$$
3-(-2)
$$

Ali Soave

Numerade Educator

00:07

Problem 110

Subtract.
$$
5-(-10)
$$

Erika Bustos

Numerade Educator

Problem 111

Subtract.
$$
-11-(-4)
$$

Erika Bustos

Numerade Educator

Problem 112

Subtract.
$$
-15-(-21)
$$

Erika Bustos

Numerade Educator

Solve. See the Concept Checks in this section. For Exercises 113 through $116,$ match the expression with the operation needed to simplify each. A letter may be used more than once and a letter may not be used at all.
a. Add the exponents.
b. Subtract the exponents.
c. Multiply the exponents.
d. Divide the exponents.
e. None of these

Erika Bustos

Numerade Educator

Problem 113

Solve. See the Concept Checks in this section. Match the expression with the operation needed to simplify each. A letter may be used more than once and a letter may not be used at all.
a. Add the exponents.
b. Subtract the exponents.
c. Multiply the exponents.
d. Divide the exponents.
e. None of these
$$
\left(x^{14}\right)^{23}
$$

Erika Bustos

Numerade Educator

Problem 114

Erika Bustos

Numerade Educator

Problem 115

Erika Bustos

Numerade Educator

Problem 116

Erika Bustos

Numerade Educator

Problem 117

Fill in the boxes so that each statement is true.
$$
x^{\square} \cdot x^{\square}=x^{12}
$$

Erika Bustos

Numerade Educator

Problem 118

Fill in the boxes so that each statement is true.
$$
\left(x^{\square}\right)^{\square}=x^{20}
$$

Erika Bustos

Numerade Educator

Problem 119

Fill in the boxes so that each statement is true.
$$
\frac{y^{\square}}{y^{\square}}=y^{7}
$$

Erika Bustos

Numerade Educator

00:37

Problem 120

Fill in the boxes so that each statement is true.
$$
\left(y^{\square}\right)^{\square} \cdot\left(y^{\square}\right)^{\square}=y^{30}
$$

Erika Bustos

Numerade Educator

Problem 121

The formula $V=x^{3}$ can be used to find the volume $V$ of a cube with side length $x$. Find the volume of a cube with side length 7 meters. (Volume is measured in cubic units.)

Erika Bustos

Numerade Educator

01:04

Problem 122

The formula $S=6 x^{2}$ can be used to find the surface area $S$ of a cube with side length $x$. Find the surface area of a cube with side length 5 meters. (Surface area is measured in square units.)

Gregory Shiver

Numerade Educator

Problem 123

To find the amount of water that a swimming pool in the shape of a cube can hold, do we use the formula for volume of the cube or surface area of the cube? (See Exercises 121 and $122 .)$

Erika Bustos

Numerade Educator