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  • Intermediate Algebra
  • Exponents and Radicals

Intermediate Algebra

Jerome E. Kaufmann, Karen L. Schwitters

Chapter 5

Exponents and Radicals - all with Video Answers

Educators

Section 1

Using Integers as Exponents

00:14

Problem 1

Answer true or false.
$\left(\frac{2}{5}\right)^{-2}=\left(\frac{5}{2}\right)^{2}$

Erika B.
Erika B.
Numerade Educator
00:18

Problem 2

Answer true or false.
$(3)^{0}(3)^{2}=9^{2}$

Erika B.
Erika B.
Numerade Educator
01:11

Problem 3

Answer true or false.
(2) $^{-4}(2)^{4}=2$

Rebecca B.
Rebecca B.
Numerade Educator
00:09

Problem 4

Answer true or false.
$\left(4^{-2}\right)^{-1}=16$

Erika B.
Erika B.
Numerade Educator
00:26

Problem 5

Answer true or false.
$\left(2^{-2} \cdot 2^{-3}\right)^{-1}=\frac{1}{16}$

Erika B.
Erika B.
Numerade Educator
00:38

Problem 6

Answer true or false.
$\left(\frac{3^{-2}}{3^{-1}}\right)^{2}=\frac{1}{9}$

Erika B.
Erika B.
Numerade Educator
01:57

Problem 7

Answer true or false.
$\frac{1}{\left(\frac{2}{3}\right)^{-3}}=\frac{8}{27}$

Rebecca B.
Rebecca B.
Numerade Educator
00:16

Problem 8

Answer true or false.
$\left(10^{4}\right)\left(10^{-6}\right)=\frac{1}{100}$

Erika B.
Erika B.
Numerade Educator
00:14

Problem 9

Answer true or false.
$\frac{x^{-6}}{x^{-3}}=x^{2}$

Erika B.
Erika B.
Numerade Educator
00:13

Problem 10

Answer true or false.
$x^{-1}-x^{-2}=\frac{x-1}{x^{2}}$

Erika B.
Erika B.
Numerade Educator
00:04

Problem 11

Simplify each numerical expression.
$\left(-\frac{3}{4}\right)^{0}$

Erika B.
Erika B.
Numerade Educator
00:34

Problem 12

Simplify each numerical expression.
$\frac{1}{\left(\frac{4}{5}\right)^{-2}}$

Erika B.
Erika B.
Numerade Educator
00:25

Problem 13

Simplify each numerical expression.
$\frac{1}{\left(\frac{3}{7}\right)^{-2}}$

Erika B.
Erika B.
Numerade Educator
00:13

Problem 14

Simplify each numerical expression.
$-\left(\frac{5}{6}\right)^{0}$

Erika B.
Erika B.
Numerade Educator
00:13

Problem 15

Simplify each numerical expression.
$2^{7} \cdot 2^{-3}$

Erika B.
Erika B.
Numerade Educator
00:09

Problem 16

Simplify each numerical expression.
$3^{-4} \cdot 3^{6}$

Erika B.
Erika B.
Numerade Educator
00:18

Problem 17

Simplify each numerical expression.
$10^{-5} \cdot 10^{2}$

Erika B.
Erika B.
Numerade Educator
00:11

Problem 18

Simplify each numerical expression.
$10^{4} \cdot 10^{-6}$

Erika B.
Erika B.
Numerade Educator
00:14

Problem 19

Simplify each numerical expression.
$10^{-1} \cdot 10^{-2}$

Erika B.
Erika B.
Numerade Educator
00:17

Problem 20

Simplify each numerical expression.
$10^{-2} \cdot 10^{-2}$

Erika B.
Erika B.
Numerade Educator
00:07

Problem 21

Simplify each numerical expression.
$\left(3^{-1}\right)^{-3}$

Erika B.
Erika B.
Numerade Educator
00:13

Problem 22

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

Erika B.
Erika B.
Numerade Educator
00:11

Problem 23

Simplify each numerical expression.
$\left(5^{3}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:12

Problem 24

Simplify each numerical expression.
$\left(3^{-1}\right)^{3}$

Erika B.
Erika B.
Numerade Educator
00:20

Problem 25

Simplify each numerical expression.
$\left(2^{3} \cdot 3^{-2}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:22

Problem 26

Simplify each numerical expression.
$\left(2^{-2} \cdot 3^{-1}\right)^{-3}$

Erika B.
Erika B.
Numerade Educator
00:26

Problem 27

Simplify each numerical expression.
$\left(4^{2} \cdot 5^{-1}\right)^{2}$

Erika B.
Erika B.
Numerade Educator
00:12

Problem 28

Simplify each numerical expression.
$\left(2^{-3} \cdot 4^{-1}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:12

Problem 29

Simplify each numerical expression.
$\left(\frac{2^{-1}}{5^{-2}}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:15

Problem 30

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

Erika B.
Erika B.
Numerade Educator
00:19

Problem 31

Simplify each numerical expression.
$\left(\frac{2^{-1}}{3^{-2}}\right)^{2}$

Erika B.
Erika B.
Numerade Educator
00:24

Problem 32

Simplify each numerical expression.
$\left(\frac{3^{2}}{5^{-1}}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:11

Problem 33

Simplify each numerical expression.
$\frac{3^{3}}{3^{-1}}$

Erika B.
Erika B.
Numerade Educator
00:15

Problem 34

Simplify each numerical expression.
$\frac{2^{-2}}{2^{3}}$

Erika B.
Erika B.
Numerade Educator
00:17

Problem 35

Simplify each numerical expression.
$\frac{10^{-2}}{10^{2}}$

Erika B.
Erika B.
Numerade Educator
00:15

Problem 36

Simplify each numerical expression.
$\frac{10^{-2}}{10^{-5}}$

Erika B.
Erika B.
Numerade Educator
00:22

Problem 37

Simplify each numerical expression.
$2^{-2}+3^{-2}$

Erika B.
Erika B.
Numerade Educator
00:34

Problem 38

Simplify each numerical expression.
$2^{-4}+5^{-1}$

Erika B.
Erika B.
Numerade Educator
00:38

Problem 39

Simplify each numerical expression.
$\left(\frac{1}{3}\right)^{-1}-\left(\frac{2}{5}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:22

Problem 40

Simplify each numerical expression.
$\left(\frac{3}{2}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:45

Problem 41

Simplify each numerical expression.
$\left(2^{-3}+3^{-2}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:42

Problem 42

Simplify each numerical expression.
$\left(5^{-1}-2^{-3}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:13

Problem 43

Simplify each expression. Express final results without using zero or negative integers as exponents.
x^{2} \cdot x^{-8}

Erika B.
Erika B.
Numerade Educator
00:09

Problem 44

Simplify each expression. Express final results without using zero or negative integers as exponents.
x^{-3} \cdot x^{-4}

Erika B.
Erika B.
Numerade Educator
00:15

Problem 45

Simplify each expression. Express final results without using zero or negative integers as exponents.
a^{3} \cdot a^{-5} \cdot a^{-1}

Erika B.
Erika B.
Numerade Educator
00:15

Problem 46

Simplify each expression. Express final results without using zero or negative integers as exponents.
b^{-2} \cdot b^{3} \cdot b^{-6}

Erika B.
Erika B.
Numerade Educator
00:08

Problem 47

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(a^{-4}\right)^{2}$

Erika B.
Erika B.
Numerade Educator
00:08

Problem 48

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(b^{4}\right)^{-3}$

Erika B.
Erika B.
Numerade Educator
00:15

Problem 49

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(x^{2} y^{-6}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:13

Problem 50

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(x^{5} y^{-1}\right)^{-3}$

Erika B.
Erika B.
Numerade Educator
00:11

Problem 50

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(x^{5} y^{-1}\right)^{-3}$

Erika B.
Erika B.
Numerade Educator
00:18

Problem 51

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(a b^{3} c^{-2}\right)^{-4}$

Erika B.
Erika B.
Numerade Educator
00:18

Problem 52

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(a^{3} b^{-3} c^{-2}\right)^{-5}$

Erika B.
Erika B.
Numerade Educator
00:23

Problem 53

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(2 x^{3} y^{-4}\right)^{-3}$

Erika B.
Erika B.
Numerade Educator
00:24

Problem 54

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(4 x^{5} y^{-2}\right)^{-2}$

Erika B.
Erika B.
Numerade Educator
00:07

Problem 55

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(\frac{x^{-1}}{y^{-4}}\right)^{-3}$

Erika B.
Erika B.
Numerade Educator
00:13

Problem 56

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(\frac{y^{3}}{x^{-4}}\right)^{-2}$

Erika B.
Erika B.
Numerade Educator
00:37

Problem 57

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(\frac{3 a^{-2}}{2 b^{-1}}\right)^{-2}$

Erika B.
Erika B.
Numerade Educator
00:42

Problem 58

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\left(\frac{2 x y^{2}}{5 a^{-1} b^{-2}}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:12

Problem 59

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\frac{x^{-6}}{x^{-4}}$

Erika B.
Erika B.
Numerade Educator
00:11

Problem 60

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\frac{a^{-2}}{a^{2}}$

Erika B.
Erika B.
Numerade Educator
00:14

Problem 61

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\frac{a^{3} b^{-2}}{a^{-2} b^{-4}}$

Erika B.
Erika B.
Numerade Educator
00:21

Problem 62

Simplify each expression. Express final results without using zero or negative integers as exponents.
$\frac{x^{-3} y^{-4}}{x^{2} y^{-1}}$

Erika B.
Erika B.
Numerade Educator
00:19

Problem 63

Find the indicated products and quotients. Express final results using positive integral exponents only.
\left(2 x y^{-1}\right)\left(3 x^{-2} y^{4}\right)

Erika B.
Erika B.
Numerade Educator
00:22

Problem 64

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\left(-4 x^{-1} y^{2}\right)\left(6 x^{3} y^{-4}\right)$

Erika B.
Erika B.
Numerade Educator
00:21

Problem 65

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\left(-7 a^{2} b^{-5}\right)\left(-a^{-2} b^{7}\right)$

Erika B.
Erika B.
Numerade Educator
00:27

Problem 66

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\left(-9 a^{-3} b^{-6}\right)\left(-12 a^{-1} b^{4}\right)$

Erika B.
Erika B.
Numerade Educator
00:20

Problem 67

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\frac{28 x^{-2} y^{-3}}{4 x^{-3} y^{-1}}$

Erika B.
Erika B.
Numerade Educator
00:19

Problem 68

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\frac{63 x^{2} y^{-4}}{7 x y^{-4}}$

Erika B.
Erika B.
Numerade Educator
00:22

Problem 69

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\frac{-72 a^{2} b^{-4}}{6 a^{3} b^{-7}}$

Erika B.
Erika B.
Numerade Educator
00:21

Problem 70

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\frac{108 a^{-5} b^{-4}}{9 a^{-2} b}$

Erika B.
Erika B.
Numerade Educator
00:34

Problem 71

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\left(\frac{35 x^{-1} y^{-2}}{7 x^{4} y^{3}}\right)^{-1}$

Erika B.
Erika B.
Numerade Educator
00:42

Problem 72

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\left(\frac{-48 a b^{2}}{-6 a^{3} b^{5}}\right)^{-2}$

Erika B.
Erika B.
Numerade Educator
00:33

Problem 73

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\left(\frac{-36 a^{-1} b^{-6}}{4 a^{-1} b^{4}}\right)^{-2}$

Erika B.
Erika B.
Numerade Educator
00:49

Problem 74

Find the indicated products and quotients. Express final results using positive integral exponents only.
$\left(\frac{8 x y^{3}}{-4 x^{4} y}\right)^{-3}$

Erika B.
Erika B.
Numerade Educator
00:21

Problem 75

Express each of the following as a single fraction involving positive exponents only.
$x^{-2}+x^{-3}$

Erika B.
Erika B.
Numerade Educator
00:15

Problem 76

Express each of the following as a single fraction involving positive exponents only.
$x^{-1}+x^{-5}$

Erika B.
Erika B.
Numerade Educator
00:18

Problem 77

Express each of the following as a single fraction involving positive exponents only.
$x^{-3}-y^{-1}$

Erika B.
Erika B.
Numerade Educator
00:17

Problem 78

Express each of the following as a single fraction involving positive exponents only.
$2 x^{-1}-3 y^{-2}$

Erika B.
Erika B.
Numerade Educator
00:18

Problem 79

Express each of the following as a single fraction involving positive exponents only.
$3 a^{-2}+4 b^{-1}$

Erika B.
Erika B.
Numerade Educator
00:17

Problem 80

Express each of the following as a single fraction involving positive exponents only.
$a^{-1}+a^{-1} b^{-3}$

Erika B.
Erika B.
Numerade Educator
00:22

Problem 81

Express each of the following as a single fraction involving positive exponents only.
$x^{-1} y^{-2}-x y^{-1}$

Erika B.
Erika B.
Numerade Educator
00:22

Problem 82

Express each of the following as a single fraction involving positive exponents only.
$x^{2} y^{-2}-x^{-1} y^{-3}$

Erika B.
Erika B.
Numerade Educator
00:13

Problem 83

Express each of the following as a single fraction involving positive exponents only.
$2 x^{-1}-3 x^{-2}$

Erika B.
Erika B.
Numerade Educator
00:22

Problem 84

Express each of the following as a single fraction involving positive exponents only.
$5 x^{-2} y+6 x^{-1} y^{-2}$

Erika B.
Erika B.
Numerade Educator
01:55

Problem 85

Is the following simplification process correct?
$\left(3^{-2}\right)^{-1}=\left(\frac{1}{3^{2}}\right)^{-1}=\left(\frac{1}{9}\right)^{-1}=\frac{1}{\left(\frac{1}{9}\right)^{1}}=9$
Could you suggest a better way to do the problem?

Rebecca B.
Rebecca B.
Numerade Educator
04:16

Problem 86

Explain how to simplify $\left(2^{-1} \cdot 3^{-2}\right)^{-1}$ and also how to simplify $\left(2^{-1}+3^{-2}\right)^{-1}$

Rebecca B.
Rebecca B.
Numerade Educator

Problem 87

Use a calculator to check your answers for Problems $1-42$.

Check back soon!
03:02

Problem 88

Use a calculator to simplify each of the following numerical expressions. Express your answers to the nearest hundredth.
(a) $\left(2^{-3}+3^{-3}\right)^{-2}$
(b) $\left(4^{-3}-2^{-1}\right)^{-2}$
(c) $\left(5^{-3}-3^{-5}\right)^{-1}$
(d) $\left(6^{-2}+7^{-4}\right)^{-2}$
(e) $\left(7^{-3}-2^{-4}\right)^{-2}$
(f) $\left(3^{-4}+2^{-3}\right)^{-3}$

Rebecca B.
Rebecca B.
Numerade Educator

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