Deck 10: Exponents and Radicals

Question 1

A negative number in the denominator becomes positive when moved to the numerator.

Answer 1

False

Question 2

When switching from scientific notation to ordinary decimal notation, if the exponent on 10 is negative, move the decimal point to the left.

Answer 2

True

Question 3

Find the indicated quotients. Express final results using positive integral exponents only. $\frac { 32 x ^ { - 2 } y ^ { - 6 } } { 8 x ^ { - 6 } y ^ { - 1 } }$

A) $4 x ^ { 4 } y ^ { 5 }$
B) $\frac { y ^ { 5 } } { 4 x ^ { 4 } }$
C) $\frac { 4 x ^ { 4 } } { y ^ { 5 } }$

Answer 3

$\frac { 4 x ^ { 4 } } { y ^ { 5 } }$

Question 4

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

A) $\frac { 3 } { 49 }$
B) $\frac { 9 } { 49 }$
C) $\frac { 49 } { 3 }$

Question 5

Simplify the expression. Express final results without using zero or negative integers as exponents. ( 3 x ⁴ y ^-5 ) ^-4

A) $\frac { y ^ { 20 } } { 81 x ^ { 16 } }$
B) $\frac { 81 x ^ { 16 } } { y ^ { 20 } }$
C) $81 y ^ { 20 } x ^ { 16 }$

Question 6

Simplify the numerical expression. 2 ^{- 4}

A) $16$
B) $\frac { 1 } { 8 }$
C) $\frac { 1 } { 16 }$

Question 7

Simplify the numerical expression. ( 4 ⁵ 5 ^{- 4} ) ^{- 1}

A) $\frac { 625 } { 1,024 }$
B) $\frac { 625 } { 3,125 }$
C) $\frac { 1,024 } { 625 }$

Question 8

Simplify the numerical expression. ( 3 ^{- 3} + 2 ^{- 2} ) ^-1

A) $\frac { 31 } { 108 }$
B) $\frac { 13 } { 108 }$
C) $\frac { 108 } { 31 }$

Question 9

Simplify the numerical expression. ( 3 ^-1 ) ^{- 3}

A) $64$
B) $27$
C) $\frac { 1 } { 27 }$

Question 10

Simplify the expression. Express final results without using zero or negative integers as exponents. a ⁴ a ^-7 a ^-2

A) $a ^ { 5 }$
B) $\frac { 1 } { a ^ { 5 } }$
C) $\frac { 1 } { a ^ { 6 } }$

Question 11

Simplify the numerical expression. $\frac { 1 } { 5 ^ { - 3 } }$

A) 125
B) 25
C) 216

Question 12

Simplify the expression. Express final results without using zero or negative integers as exponents. ( a b ² c ^{- 1} ) ^{- 5}

A) $\frac { c ^ { 5 } } { a ^ { 5 } b ^ { 10 } }$
B) $\frac { a ^ { 5 } b ^ { 10 } } { c ^ { 5 } }$
C) $a ^ { 5 } b ^ { 10 } c ^ { 5 }$

Question 13

If b is a nonzero real number, then $b ^ { 0 } = 0$ .

Question 14

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

A) 16
B) -8
C) 81

Question 15

Simplify the numerical expression. $-$ 10 - 4

A) $- \frac { 1 } { 1,000 }$
B) $- \frac { 1 } { 10,000 }$
C) $- 10,000$

Question 16

Find the indicated product. Express final results using positive integral exponents only. (3 xy ^{- 2})(8 x ^{- 3} y ⁷)

A) $\frac { x ^ { 2 } } { 24 y ^ { 5 } }$
B) $24 x ^ { 2 } y ^ { 5 }$
C) $\frac { 24 y ^ { 5 } } { x ^ { 2 } }$

Question 17

Simplify the numerical expression. 3⁹ 3^-4

A) 1,594,323
B) 243
C) 729

Question 18

The power of a product is equal to the product of each factor to the same power.

Question 19

Simplify the numerical expression. ( 3 2 . 7 -1 ) 2

A) $\frac { 81 } { 49 }$
B) $3,969$
C) $\frac { 27 } { 49 }$

Question 20

Simplify the numerical expression. 5 ^{- 2} + 2 ^{- 2}

A) $\frac { 100 } { 29 }$
B) $\frac { 20 } { 29 }$
C) $\frac { 29 } { 100 }$

Question 21

Express the following as a single fraction involving positive exponents only. 4 x ^{- 3} - 5 x ^{- 7}

A) $\frac { 4 x ^ { 4 } - 5 } { x ^ { 7 } }$
B) $4 x ^ { 7 } - 5 x ^ { 3 }$
C) $\frac { 4 x ^ { 4 } - 5 } { x ^ { 6 } }$

Question 22

Write 7,000,000 in scientific notation.

A) $( 0.7 ) ( 10 ) ^ { 6 }$
B) $( 7 ) ( 10 ) ^ { 6 }$
C) $( 7 ) ( 10 ) ^ { 7 }$
D) $( 0.7 ) ( 10 ) ^ { 7 }$
E) $( 7 ) ( 10 ) ^ { 5 }$

Question 23

Simplify the numerical expression. 5 ⁸ 5 ^{- 3}

Question 24

Simplify the numerical expression. ( 4 ^-1 ) ^{- 2}

Question 25

Simplify the numerical expression. ( 3 ² 2 ^-1 ) ² Please enter your answer as a fraction.

Question 26

Simplify the numerical expression. 2 ^{- 4} Please enter your answer as a fraction.

Question 27

Simplify the numerical expression. ( 4 ⁵ 5 ^{- 4} ) ^-1 Please enter your answer as a fraction.

Question 28

Simplify the numerical expression. 10 - 2 Please enter your answer as a fraction.

Question 29

Simplify the expression. Express final results without using zero or negative integers as exponents. ( 2 x ⁴ y ^-5 ) ^-3 Please enter your answer as a fraction.

Question 30

Simplify the expression. Express final results without using zero or negative integers as exponents. a ⁶ a ^-8 a ^-3 Please enter your answer as a fraction.

Question 31

Simplify the numerical expression. ( 3 ^-3 + 2 ^-2 ) ^-1 Please enter your answer as a fraction.

Question 32

Simplify the numerical expression. 2 ^{- 2} + 3 ^{- 2} Please enter your answer as a fraction.

Question 33

Find the indicated product. Express final results using positive integral exponents only. (4 xy ^{- 4})(9 x ^{- 4} y ⁸) Please enter your answer as a fraction.

Question 34

Write in ordinary decimal notation.

Question 35

Simplify the numerical expression.

Question 36

Find the indicated quotients. Express final results using positive integral exponents only. $\left( \frac { 28 x ^ { - 2 } y ^ { - 3 } } { 4 x ^ { 7 } y ^ { 8 } } \right) ^ { - 1 }$

A) $\frac { 7 } { x ^ { 9 } y ^ { 11 } }$
B) $7 x ^ { 9 } y ^ { 11 }$
C) $\frac { x ^ { 9 } y ^ { 11 } } { 7 }$

Question 37

Write $( 5.26 ) ( 10 ) ^ { - 2 }$ in ordinary decimal notation.

A) 0.0521
B) 0.526
C) 0.00526
D) 0.0531
E) 0.0526

Question 38

Simplify the numerical expression.

Question 39

Simplify the numerical expression. Please enter your answer as a fraction.

Question 40

Simplify the expression. Express final results without using zero or negative integers as exponents. ( a b ³ c ^{- 1} ) ^{- 4} Please enter your answer as a fraction.

Question 41

Evaluate. $\sqrt [ 3 ] { \frac { 1 } { 8 } }$

A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 7 }$
D) $\frac { 2 } { 3 }$

Question 42

Evaluate. $\sqrt { 81 }$

A) 11
B) 10
C) 8
D) 9

Question 43

Evaluate. $\sqrt [ 3 ] { - 64 }$

A) $-$ 4
B) $-$ 8
C) 8
D) 4

Question 44

Evaluate. $\sqrt [ 6 ] { 2 ^ { 6 } }$

A) -4
B) 8
C) 2
D) 4

Question 45

Change the radical to simplest radical form. $5 \sqrt { 180 }$

A) $25 \sqrt { 30 }$
B) $30 \sqrt { 5 }$
C) $6 \sqrt { 5 }$
D) $5 \sqrt { 5 }$

Question 46

Change the radical to simplest radical form. $- \frac { 3 } { 16 } \sqrt { 20 }$

A) $- \frac { \sqrt { 5 } } { 8 }$
B) $- 3 \sqrt { 5 }$
C) $3 \sqrt { 5 }$
D) $- \frac { 3 \sqrt { 5 } } { 8 }$

Question 47

Evaluate. $\sqrt [ 3 ] { 64 }$

A) 4
B) 16
C) 1
D) 8

Question 48

Change the radical to simplest radical form. $\sqrt { 45 }$

A) 22.5
B) $5 \sqrt { 3 }$
C) $3 \sqrt { 5 }$
D) 15

Question 49

Change the radical to simplest radical form. $\frac { 5 } { 8 } \sqrt { 192 }$

A) $40 \sqrt { 3 }$
B) $5 \sqrt { 3 }$
C) $3 \sqrt { 5 }$
D) $24 \sqrt { 5 }$

Question 50

The square root of a number is one of its two equal factors.

Question 51

Write 70,000,000 in scientific notation.

Question 52

Find the indicated quotients. Express final results using positive integral exponents only. Please enter your answer as a fraction.

Question 53

Find the indicated quotients. Express final results using positive integral exponents only. Please enter your answer as a fraction.

Question 54

The cube root of a number can be a negative number.

Question 55

Change the radical to simplest radical form. $\sqrt { \frac { 10 } { 7 } }$

A) $7 \sqrt { 70 }$
B) $\frac { \sqrt { 70 } } { 7 }$
C) $\frac { \sqrt { 10 } } { 7 }$
D) $\frac { \sqrt { 10 } } { \sqrt { 7 } }$

Question 56

The number under the radical sign is called the radical.

Question 57

Change the radical to simplest radical form. $\sqrt { \frac { 19 } { 64 } }$

A) $19 \sqrt { 8 }$
B) $8 \sqrt { 19 }$
C) $\frac { \sqrt { 19 } } { 8 }$
D) $\frac { \sqrt { 8 } } { 19 }$

Question 58

Evaluate. $- \sqrt { \frac { 81 } { 16 } }$

A) $\frac { 9 } { 4 }$
B) $\frac { 4 } { 9 }$
C) $- \frac { 9 } { 4 }$
D) $- \frac { 9 } { 16 }$

Question 59

Express the following as a single fraction involving positive exponents only. 2 x ^{- 3} - 3 x ^{- 5} Please enter your answer as a fraction.

Question 60

$\frac { 5 \sqrt { 27 } } { 9 }$ is in simplest radical form.

Question 61

Change the radical to simplest radical form.

Question 62

Find, to the nearest square yard, the area of a triangular plot of ground that measures 15 yards by 20 yards by 25 yards.

A) 150 square yards
B) 300 square yards
C) 37.5 square yards
D) 75 square yards

Question 63

Evaluate.

Question 64

Evaluate.

Question 65

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 21 } } { \sqrt [ 3 ] { 7 } }$

A) $\sqrt [ 3 ] { 3 }$
B) 3
C) $\sqrt [ 3 ] { 14 }$
D) $7 \sqrt [ 3 ] { 21 }$

Question 66

Change the radical to simplest radical form.

Question 67

Evaluate.

Question 68

Change the radical to simplest radical form.

Question 69

Change the radical to simplest radical form.

Question 70

The period of a pendulum is the time it takes to swing from one side to the other side and back. The formula $T = 2 \pi \sqrt { \frac { L } { 32 } }$ where T represents the time in seconds and L the length in feet, can be used to determine the period of a pendulum (see the figure). Find the period of a 4.5-feet pendulum. Express your answer to the nearest tenth of a second.

A) 2.7 seconds
B) 3.1 seconds
C) 2.6 seconds
D) 2.4 seconds

Question 71

Change the radical to simplest radical form.

Question 72

Change the radical to simplest radical form.

Question 73

Using f = 0.35 as a coefficient of friction, determine how fast a car was traveling if it skidded D = 300 feet. Use the formula $S = \sqrt { 30 D f }$ Express your answer to the nearest mile per hour.

A) 63 miles per hour
B) 51 miles per hour
C) 43 miles per hour
D) 56 miles per hour

Question 74

Change the radical to simplest radical form.

Question 75

Change the radical to simplest radical form. $- 7 \sqrt [ 3 ] { 54 }$

A) $14 \sqrt [ 3 ] { 3 }$
B) $- 21 \sqrt [ 3 ] { 2 }$
C) 21
D) $- 7 \sqrt [ 3 ] { 2 }$

Question 76

Change the radical to simplest radical form. $\frac { \sqrt { 15 } } { \sqrt { 33 } }$

A) $11 \sqrt { 55 }$
B) $\sqrt { \frac { 15 } { 33 } }$
C) $\frac { \sqrt { 55 } } { 11 }$
D) $\frac { \sqrt { 55 } } { 33 }$

Question 77

Change the radical to simplest radical form. $\sqrt [ 3 ] { 54 }$

A) 3
B) $2 \sqrt [ 3 ] { 3 }$
C) $3 \sqrt [ 3 ] { 2 }$
D) $\sqrt [ 3 ] { 2 }$

Question 78

Evaluate.

Question 79

Change the radical to simplest radical form. $- \frac { 4 \sqrt { 20 } } { 6 \sqrt { 35 } }$

A) $\frac { 35 \sqrt { 20 } } { 6 }$
B) $- \frac { \sqrt { 35 } } { 21 }$
C) $4 \sqrt { 7 }$
D) $- \frac { 4 \sqrt { 7 } } { 21 }$

Question 80

Find, to the nearest square yard, the area of a triangular plot of ground that measures 15 yards by 20 yards by 25 yards. __________ square yards