Deck 7: Rational Exponents, Radicals, and Complex Numbers

Question 1

Find each root.

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Answer 1

10

Question 2

Find each root.
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Answer 2

9/11

Question 3

Find each root.
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Answer 3

-8

Question 4

Find each root.
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Question 5

Find each root.
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Question 6

Find each root.
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Question 7

Find each root.
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Question 8

Find each root.
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Question 9

Find each root.
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Question 10

Find each root.
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Question 11

Find each root.
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Question 12

Find each root.
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Question 13

Simplify. Assume that the variables represent any real numbers.
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Question 14

Simplify. Assume that the variables represent any real numbers.
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Question 15

Simplify. Assume that the variables represent any real numbers.
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Question 16

Simplify. Assume that the variables represent any real numbers.
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Question 17

If $f(x) = \sqrt{3x-3} and g(x) = \sqrt[3]{x-4}$ , find each function value.
-f(4)

Question 18

If $f(x) = \sqrt{3x-3} and g(x) = \sqrt[3]{x-4}$ , find each function value.
-f(7)

Question 19

If $f(x) = \sqrt{3x-3} and g(x) = \sqrt[3]{x-4}$ , find each function value.
-g(5)

Question 20

If $f(x) = \sqrt{3x-3} and g(x) = \sqrt[3]{x-4}$ , find each function value.
-g(12)

Question 21

Use radical notation to write each expression. Simplify if possible
-81^1/2

Question 22

Use radical notation to write each expression. Simplify if possible
-64^1/3

Question 23

Use radical notation to write each expression. Simplify if possible
- ${(\frac1{81})^{1/4}}$

Question 24

Use radical notation to write each expression. Simplify if possible
-(3m)^1/5

Question 25

Use radical notation to write each expression. Simplify if possible
-(9x¹⁰)^1/2

Question 26

Use radical notation to write each expression. Simplify if possible
-(-8)^5/3

Question 27

Use radical notation to write each expression. Simplify if possible
-(6x - 1)^2/3

Question 28

Use radical notation to write each expression. Simplify if possible
- $(\frac{25}{36})^{3/2}$

Question 29

Write with positive exponents. Simplify if possible.
- $25^{-1/2}$

Question 30

Write with positive exponents. Simplify if possible.
- $(25)^{-5/4}$

Question 31

Write with positive exponents. Simplify if possible.
- $x^{-1/5}$

Question 32

Write with positive exponents. Simplify if possible.
- $\frac4{7y^{-2/3}}$

Question 33

Use the properties of exponents to simplify each expression. Write with positive exponents.
- $x^{7/5} \cdot x^{-3/5}$

Question 34

Use the properties of exponents to simplify each expression. Write with positive exponents.
- $10^{2/3} \cdot 10^{1/9}$

Question 35

Use the properties of exponents to simplify each expression. Write with positive exponents.
- $(81^{1/4}x^{3/4})^2$

Question 36

Use the properties of exponents to simplify each expression. Write with positive exponents.
- $\frac{(x^2y)^{1/4}}{x^{-3/2}y^{3/8}}$

Question 37

Use rational exponents to simplify each radical. Assume that all variables represent positive numbers.
- $\sqrt[4]{(y-7)^2}$

Question 38

Use rational exponents to simplify each radical. Assume that all variables represent positive numbers.
- $\sqrt[6]{a^3b^6}$

Question 39

Use rational exponents to write as a single radical expression.
- $\sqrt[4]{x} \cdot \sqrt[3]{x^2} \cdot \sqrt[6]{x^5}$

Question 40

Use rational exponents to write as a single radical expression.
- $\sqrt[5]{a} \cdot \sqrt[4]{3b}$

Question 41

Simplify.
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Question 42

Simplify.
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Question 43

Simplify.
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Question 44

Simplify.
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Question 45

Simplify.
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Question 46

Simplify.
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Question 47

Simplify.
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Question 48

Simplify.
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Question 49

Simplify.
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Question 50

Simplify.
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Question 51

Simplify.
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Question 52

Simplify.
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Question 53

Simplify.
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Question 54

Simplify.
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Question 55

Simplify.
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Question 56

Simplify.
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Question 57

Find the distance between each pair of points.
-(6,2) and (9,6)

Question 58

Find the distance between each pair of points.
- $(\sqrt{2},0) and (0,-\sqrt{3})$

Question 59

Find the midpoint of each line segment whose points are given
-(7,-9) and (1,5)

Question 60

Find the midpoint of each line segment whose points are given
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Question 61

Add or subtract as indicated.
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Question 62

Add or subtract as indicated.
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Question 63

Add or subtract as indicated.
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Question 64

Add or subtract as indicated.
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Question 65

Add or subtract as indicated.
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Question 66

Add or subtract as indicated.
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Question 67

Add or subtract as indicated.
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Question 68

Add or subtract as indicated.
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Question 69

Add or subtract as indicated.
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Question 70

Add or subtract as indicated.
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Question 71

Multiply. Then simplify if possible.
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Question 72

Multiply. Then simplify if possible.
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Question 73

Multiply. Then simplify if possible.
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Question 74

Multiply. Then simplify if possible.
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Question 75

Multiply. Then simplify if possible.
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Question 76

Multiply. Then simplify if possible.
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Question 77

Multiply. Then simplify if possible.
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Question 78

Multiply. Then simplify if possible.
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Question 79

Multiply. Then simplify if possible.
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Question 80

Multiply. Then simplify if possible.
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