Deck 5: Exponents and Radicals

Question 1

Simplify the numerical expression. $$15 ( - 6 ) ^ { 4 } - 3 ( - 5 ) ^ { 3 } + 7 ( - 4 ) + 12$$

A)19,799
B)6,593
C)-16
D)-331
E)65,613,359

Answer 1

19,799

Question 2

Simplify the expression. Express the final result without using zero or negative integers as exponents. $$a ^ { 4 } \cdot a ^ { - 5 } \cdot a ^ { - 2 }$$

A) $\frac { a ^ { 4 } } { a ^ { 7 } }$
B) $\frac { 1 } { a ^ { 3 } }$
C) $\frac { 1 } { a ^ { 4 } }$
D) $a$
E) $\frac { a ^ { 4 } } { a ^ { 10 } }$

Answer 2

$\frac { 1 } { a ^ { 3 } }$

Question 3

Find a rational approximation, to the nearest tenth, for the radical expression. $2 \sqrt { 5 } + 5 \sqrt { 5 }$

A) $13.8$
B) $19.2$
C) $16.7$
D) $16.8$
E) $15.7$

Answer 3

$15.7$

Question 4

Simplify the expression. $\left( 7 x ^ { 8 } \right) ^ { 2 }$

A) $7 x ^ { 16 }$
B) $7 x ^ { 8 }$
C) $49 x ^ { 17 }$
D) $49 x ^ { 16 }$
E) $49 x ^ { 15 }$

Question 5

Simplify the numerical expression. $$- 10 ^ { - 3 }$$

A) $\frac { 1 } { 100 }$
B) $- 1,000$
C) $- \frac { 3 } { 1,000 }$
D) $\frac { 1 } { 1,000 }$
E) $- \frac { 1 } { 1,000 }$

Question 6

Use a calculator to find a rational approximation of the square root. Express your answer to the nearest hundredth. $\sqrt { 27 }$

A) $2.60$
B) $5.40$
C) $5.20$
D) $5.10$
E) $10.39$

Question 7

Find the indicated product. Express the final result using positive integral exponents only. $$\left( 2 x y ^ { - 4 } \right) \left( 4 x ^ { - 4 } y ^ { 7 } \right)$$

A) $\frac { 8 y ^ { 3 } } { x ^ { 3 } }$
B) $8 x ^ { - 3 } y ^ { 3 }$
C) $8 x ^ { 3 } y ^ { 3 }$
D) $\frac { x ^ { 3 } } { 8 y ^ { 3 } }$
E) $\frac { y ^ { 7 } } { 8 x y ^ { 8 } }$

Question 8

Write the quotient as the quotient of two radicals and simplify. $\sqrt { \frac { 169 } { 100 } }$

A) $\frac { 7 } { 10 }$
B) $\frac { 10 } { 7 }$
C) $\frac { 13 } { 10 }$
D) $\frac { 10 } { 13 }$
E) $\frac { 169 } { 10 }$

Question 9

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

A) $- \frac { 1 } { x ^ { 10 } }$
B) $4 x ^ { 7 } - 5 x ^ { 3 }$
C) $\frac { 4 x ^ { 4 } - 5 } { x ^ { 7 } }$
D) $\frac { 4 x ^ { 4 } - 5 } { x ^ { 6 } }$
E) $\frac { 1 } { 4 x ^ { 7 } - 5 x ^ { 3 } }$

Question 10

Simplify the numerical expression.

Question 11

Find the indicated quotient. Express the final result using positive integral exponents only. $$\left( \frac { 63 x ^ { - 2 } y ^ { - 2 } } { 9 x y ^ { 7 } } \right) ^ { - 2 }$$

A) $\frac { 1 } { 49 x ^ { 16 } y ^ { 18 } }$
B) $49 x ^ { 4 } y ^ { 5 }$
C) $49 x ^ { 16 } y ^ { 10 }$
D) $\frac { x ^ { 16 } y ^ { 18 } } { 49 }$
E) $\frac { 49 } { x ^ { 16 } y ^ { 18 } }$

Question 12

Find a rational approximation, to the nearest tenth, for the radical expression. $7 \sqrt { 3 } - 8 \sqrt { 3 } + 10 \sqrt { 3 } - 7 \sqrt { 3 } - 9 \sqrt { 3 }$

A) $- 8.8$
B) $- 11.4$
C) $- 13.1$
D) $- 11.3$
E) $- 12.1$

Question 13

Simplify the radical. $\sqrt { 32 }$

A) $4 \sqrt { 3 }$
B) $5 \sqrt { 3 }$
C) $16$
D) $4 \sqrt { 2 }$
E) $5 \sqrt { 2 }$

Question 14

Find the indicated product. Express the final result using positive integral exponents only. $$3 x y ^ { - 2 } 5 x ^ { - 3 } y ^ { 4 }$$

A) $\frac { y ^ { 4 } } { 15 x y ^ { 5 } }$
B) $15 x ^ { - 2 } y ^ { 2 }$
C) $\frac { x ^ { 2 } } { 15 y ^ { 2 } }$
D) $15 x ^ { 2 } y ^ { 2 }$
E) $\frac { 15 y ^ { 2 } } { x ^ { 2 } }$

Question 15

Change the radical to simplest radical form. $- \frac { 6 \sqrt { 12 } } { 21 \sqrt { 21 } }$

A) $- \frac { \sqrt { 21 } } { 49 }$
B) $\frac { 21 } { 21 } \sqrt { 12 }$
C) $4 \sqrt { 7 }$
D) $- \frac { 4 } { 49 } \sqrt { 7 }$
E) $- \frac { 2 } { 7 } \frac { \sqrt { 4 } } { \sqrt { 7 } }$

Question 16

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

A) $\frac { 9 } { 8 }$
B) $\frac { 8 } { 9 }$
C) $\frac { 1 } { 6 }$
D) $\frac { 1 } { 3 }$
E) $\frac { 3 } { 2 }$

Question 17

Simplify the expression. $\sqrt { 200 } + \sqrt { 700 } - \sqrt { 175 }$

A) $10 \sqrt { 2 } - 5 \sqrt { 7 }$
B) $10 \sqrt { 2 } + 5 \sqrt { 7 }$
C) $2 \sqrt { 2 } + 5 \sqrt { 7 }$
D) $5 \sqrt { 2 } + 2 \sqrt { 7 }$
E) $2 \sqrt { 2 } - 5 \sqrt { 7 }$

Question 18

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

A) $\frac { x ^ { 3 } } { y ^ { 12 } }$
B) $\frac { y ^ { 7 } } { x ^ { 4 } }$
C) $\frac { x ^ { 4 } } { y ^ { 12 } }$
D) $\frac { y ^ { 12 } } { x ^ { 3 } }$
E) $\frac { x ^ { 4 } } { y ^ { 7 } }$

Question 19

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

A) $\frac { x ^ { 6 } - 4 x ^ { 4 } - 5 } { x ^ { 7 } }$
B) $- \frac { x } { 4 x ^ { 7 } + 5 x ^ { 3 } }$
C) $\frac { 4 x ^ { 4 } + 5 } { x ^ { 6 } }$
D) $x ^ { 6 } - 4 x ^ { 7 } - 5 x ^ { 3 }$
E) $- \frac { 1 } { x ^ { 10 } }$

Question 20

Change the radical to simplest radical form. $\frac { \sqrt { 40 } } { \sqrt { 88 } }$

A) $11 \sqrt { 55 }$
B) $\frac { \sqrt { 55 } } { 11 }$
C) $\frac { 8 \sqrt { 55 } } { 11 }$
D) $\sqrt { \frac { 40 } { 88 } }$
E) $\frac { \sqrt { 55 } } { 88 }$

Question 21

Simplify the expression. $\sqrt [ 3 ] { 128 x ^ { 4 } y ^ { 5 } } - \sqrt [ 3 ] { 54 x ^ { 4 } y ^ { 5 } }$

A) $2 x y ^ { 2 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$
B) $- 2 x y ^ { 2 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$
C) $2 x ^ { 2 } y ^ { 3 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$
D) $- x y ^ { 2 } \sqrt [ 3 ] { 4 x y }$
E) $x y \sqrt [ 3 ] { 2 x y ^ { 2 } }$

Question 22

Find the following product and express your answer in simplest radical form. $\frac { \sqrt { 42 } } { 7 \sqrt { 6 } + 6 \sqrt { 7 } }$

A) $\sqrt { 6 } - \sqrt { 7 }$
B) $\sqrt { 7 } - \sqrt { 6 }$
C) $\frac { \sqrt { 42 } } { \sqrt { 7 } + \sqrt { 6 } }$
D) $\sqrt { 7 } + \sqrt { 6 }$
E) $\frac { 1 } { \sqrt { 7 } + \sqrt { 6 } }$

Question 23

Rationalize the denominator and simplify. The variable represents a positive real number. $\frac { \sqrt { x } } { \sqrt { x } - 10 }$

A) $\frac { 10 \sqrt { x } } { x - 100 }$
B) $\frac { x + 10 \sqrt { x } } { x - 10 }$
C) $\sqrt { x }$
D) $\frac { 11 x } { x - 100 }$
E) $\frac { x + 10 \sqrt { x } } { x - 100 }$

Question 24

Find the following product and express your answer in simplest radical form. $( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )$

A) $- 112 \sqrt { 77 } - 44 \sqrt { 7 } + 980 \sqrt { 11 } + 385$
B) $112 \sqrt { 77 } - 44 \sqrt { 11 } - 980 \sqrt { 7 } + 385$
C) $16 \sqrt { 7 } + 4 \sqrt { 11 } - 385$
D) $112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385 \sqrt { 343 }$
E) $112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385$

Question 25

Simplify the expression by using the distributive property. $6 \sqrt { 11 } + 2 \sqrt { 11 }$

A) $30$
B) $12 \sqrt { 11 }$
C) $8 \sqrt { 11 }$
D) $4 \sqrt { 11 }$
E) $7 \sqrt { 11 }$

Question 26

Multiply and simplify where possible. $\sqrt { 8 } \sqrt { 20 }$

A) $10 \sqrt { 10 }$
B) $2 \sqrt { 10 }$
C) $4 \sqrt { 10 }$
D) $10 \sqrt { 2 }$
E) $8 \sqrt { 10 }$

Question 27

Use the distributive property to help simplify the expression. $2 \sqrt [ 3 ] { 2 } + 2 \sqrt [ 3 ] { 54 } - 2 \sqrt [ 3 ] { 16 }$

A) $6 \sqrt [ 3 ] { 2 }$
B) $- 4 \sqrt [ 3 ] { 2 }$
C) $- 4 \sqrt [ 3 ] { 3 }$
D) $4 \sqrt [ 3 ] { 2 }$
E) $4 \sqrt [ 3 ] { 3 }$

Question 28

Perform the indicated operation and express your answer in simplest radical form. $\sqrt { 5 } \sqrt [ 3 ] { 5 }$

A) $\sqrt [ 5 ] { 125 }$
B) $\sqrt [ 5 ] { 3,125 }$
C) $\sqrt [ 6 ] { 25 }$
D) $\sqrt [ 6 ] { 5 }$
E) $\sqrt [ 6 ] { 3,125 }$

Question 29

Use the distributive property to help simplify the expression. $\frac { 1 } { 3 } \sqrt { 2 } - \frac { 1 } { 4 } \sqrt { 18 }$

A) $\frac { 12 } { 5 } \sqrt { 2 }$
B) $- \frac { 5 } { 12 } \sqrt { 2 }$
C) $- \frac { 5 } { 12 } \sqrt { 5 }$
D) $\frac { 5 } { 12 } \sqrt { 5 }$
E) $\frac { 5 } { 12 } \sqrt { 2 }$

Question 30

Johannes Kepler discovered that a planet's mean distance $R$ from the sun (in astronomical units)is related to its period $T$ (in years)by the formula $R = \sqrt [ 3 ] { \frac { T ^ { 2 } } { k } }$ Find $R$ when $T = 1.881$ and $k = 1.002$ .

A)1.52 AU
B)1.22 AU
C)1.37 AU
D)1.35 AU
E)1.45 AU

Question 31

Rationalize the denominator and simplify. $\frac { 21 } { \sqrt { 21 } + 1 }$

A) $\frac { 21 ( \sqrt { 21 } - 1 ) } { 20 }$
B) $\frac { 21 \sqrt { 21 } - 1 } { 20 }$
C) $\frac { 20 ( \sqrt { 21 } - 1 ) } { 21 }$
D) $\frac { \sqrt { 21 } - 21 } { 20 }$
E) $21 ( \sqrt { 21 } - 1 )$

Question 32

Simplify the expression. All variables represent positive numbers. $\sqrt { 2 x ^ { 3 } } - \sqrt { 18 x ^ { 3 } }$

A) $- x \sqrt { 3 x }$
B) $- x \sqrt { 2 x }$
C) $- 2 x \sqrt { 2 x }$
D) $- 2 x \sqrt { 3 x }$
E) $- 2 x \sqrt { 5 x }$

Question 33

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 14 } } { \sqrt [ 3 ] { 7 } }$

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

Question 34

The formula $s = k \sqrt { d }$ relates the speed $s$ (in mph)of a car and the distance $d$ of the skid when a driver hits the brakes. How far will a car skid if it is going 48 mph on dry pavement? On dry pavement, $k = 5.34$ .

A)about 59 ft
B)about 76 ft
C)about 99 ft
D)about 81 ft
E)about 70 ft

Question 35

Find the following product and express your answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )$

A) $\sqrt { 5 } - \sqrt { 3 }$
B) $\sqrt { 3 } - 7$
C) $\sqrt { 5 } + \sqrt { 7 }$
D) $\sqrt { 15 } + \sqrt { 35 }$
E) $\sqrt { 15 } - \sqrt { 35 }$

Question 36

The power generated by a windmill is related to the speed of the wind by the formula $S = \sqrt [ 3 ] { \frac { P } { 0.02 } }$ , where $S$ is the speed of the wind (in mph)and $P$ is the power (in watts). Find the speed of the wind when the windmill is producing 413 watts of power.

A)27.07 mph
B)28.99 mph
C)28.25 mph
D)27.44 mph
E)27.56 mph

Question 37

Solve the equation. Check all solutions. $\sqrt { x } = 9$

A)81
B)41
C)9
D)79
E)no solution

Question 38

Multiply and simplify where possible. $( - 17 \sqrt { 17 } ) ( - 49 \sqrt { 343 } )$

A) $5,831 \sqrt { 7 }$
B) $833 \sqrt { 119 }$
C) $17 \sqrt { 119 }$
D) $5,831 \sqrt { 119 }$
E) $343 \sqrt { 119 }$

Question 39

Perform the multiplication. The variable represents a positive number. $\sqrt { y } ( \sqrt { 6 y } - 2 )$

A) $y \sqrt { 2 } - 6 \sqrt { y }$
B) $y \sqrt { 6 } + 2 \sqrt { y }$
C) $y \sqrt { 6 } - 2 \sqrt { y }$
D) $6 y - 2 \sqrt { y }$
E) $6 \sqrt { y } - y \sqrt { 2 }$

Question 40

Simplify the expression. $\sqrt { 8 x y ^ { 3 } } - \sqrt { 75 y ^ { 3 } x }$

A) $2 y ^ { 2 } \sqrt { 2 x y } - 5 y ^ { 2 } \sqrt { 3 x y }$
B) $2 y \sqrt { 2 x y } - 5 y \sqrt { 3 x y }$
C) $3 y \sqrt { 2 x y } - 5 y \sqrt { 3 x y }$
D) $2 y \sqrt { 4 x y } - 5 y \sqrt { 15 x y }$
E)none of the above

Question 41

The formula $s = k \sqrt { d }$ relates the speed $s$ (in mph)of a car and the distance $d$ of the skid when a driver hits the brakes. On wet pavement, $k = 3.24$ . How far will a car skid if it is going 51 mph?

A)about 225 ft
B)about 282 ft
C)about 248 ft
D)about 203 ft
E)about 236 ft

Question 42

Change the radical to an exponential expression. $\sqrt { m ^ { 2 } + k ^ { 2 } }$

A) $\left( m ^ { 2 } + k ^ { 2 } \right) ^ { 2 }$
B) $m ^ { \frac { 3 } { 2 } } + k ^ { \frac { 3 } { 2 } }$
C) $( m + k ) ^ { \frac { 1 } { 2 } }$
D) $\left( m ^ { 2 } + k ^ { 2 } \right) ^ { \frac { 1 } { 2 } }$
E) $( m + k ) ^ { \frac { 3 } { 2 } }$

Question 43

Write $x ^ { \frac { 3 } { 4 } } y ^ { \frac { 1 } { 4 } }$ in radical form. For example, $3 x ^ { \frac { 2 } { 3 } } = 3 \sqrt [ 3 ] { x ^ { 2 } }$ .

A) $\frac { 1 } { \sqrt [ 4 ] { x ^ { 3 } y } }$
B) $\sqrt [ 4 ] { x ^ { 3 } y }$
C) $\sqrt { x ^ { 4 } y }$
D) $y \sqrt [ 4 ] { x ^ { 3 } }$
E) $\sqrt [ 3 ] { x ^ { 4 } y }$

Question 44

Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 3 ] { 8 } } { \sqrt [ 4 ] { 8 } }$

A) $- \sqrt { 8 }$
B) $\sqrt [ 12 ] { 8 }$
C) $\frac { 1 } { \sqrt [ 12 ] { 8 } \sqrt { 8 } }$
D) $\sqrt [ 7 ] { 8 }$
E) $\sqrt [ 12 ] { 64 }$

Question 45

Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.

A) $\sqrt [ 3 ] { 8 }$
B) $\sqrt [ 3 ] { 512 }$
C) $\sqrt [ 4 ] { 8 }$
D) $\sqrt [ 4 ] { 512 }$
E) $\sqrt [ 4 ] { 64 }$

Question 46

Simplify the expression. $\left( - \frac { 243 } { 1024 } \right) ^ { \frac { 1 } { 5 } }$

A) $- \frac { 81 } { 256 }$
B) $- \frac { 3 } { 4 }$
C) $- \frac { 4 } { 3 }$
D) $- \frac { 243 } { 4 }$
E) $- \frac { 5 } { 6 }$

Question 47

Change the expression into radical notation.

Question 48

The number of wrenches that can be produced at a given price can be predicted by the formula $s = \sqrt { 65 x }$ , where $s$ is the supply (in thousands)and $X$ is the price (in dollars). If the demand $d$ for the wrenches can be predicted by the formula $d = \sqrt { 324 - 4 x ^ { 2 } }$ , find the equilibrium price.

A)$6
B)$5
C)$4
D)None of the above

Question 49

Write $- \sqrt [ 9 ] { x + y }$ using positive rational exponents.

A) $- ( x + y ) ^ { 9 }$
B) $( - x - y ) ^ { \frac { 1 } { 9 } }$
C) $- ( x + y ) ^ { \frac { 2 } { 9 } }$
D) $( x + y ) ^ { - \frac { 1 } { 9 } }$
E) $- ( x + y ) ^ { \frac { 1 } { 9 } }$

Question 50

The formula $T = 2 \pi \sqrt { \frac { L } { 32 } }$ represents the period of a pendulum T (in seconds), L - the length of the pendulum (in feet). Solve the formula for L if T = 39.4384 sec, π = 3.14.

A)78.8768 feet
B)100.48 feet
C)128 feet
D)32 feet

Question 51

Simplify the expression. $2 ^ { \frac { 4 } { 5 } } 2 ^ { \frac { 6 } { 5 } }$

A)16
B) $2 ^ { \frac { 1 } { 5 } }$
C)2
D)4
E)81

Question 52

Simplify the expression. $16 ^ { \frac { 3 } { 2 } }$

A)16
B)7,776
C)36
D)11
E)1,024

Question 53

Simplify the expression. $125 ^ { \frac { 1 } { 3 } }$

A) $\frac { 1 } { 5 }$
B) $12$
C) $\frac { 1 } { 28 }$
D) $2$
E) $5$

Question 54

Write $4 x ^ { \frac { 2 } { 7 } }$ in radical form. For example, $3 x ^ { \frac { 2 } { 3 } } = 3 \sqrt [ 3 ] { x ^ { 2 } }$

A) $\frac { 1 } { 4 \sqrt [ 7 ] { x ^ { 2 } } }$
B) $\sqrt { x ^ { 5 } }$ $\sqrt { x ^ { 7 } }$
C) $4 \sqrt [ 7 ] { x ^ { 2 } }$
D) $4 \sqrt [ 2 ] { x ^ { 7 } }$
E) $\sqrt [ 7 ] { 4 x ^ { 2 } }$

Question 55

Write $2 \sqrt [ 13 ] { y ^ { 11 } }$ using positive rational exponents. For example, $\sqrt { a b } = ( a b ) ^ { \frac { 1 } { 2 } } = a ^ { \frac { 1 } { 2 } } b ^ { \frac { 1 } { 2 } }$ .

A) $4 y$
B) $( 4 y ) ^ { \frac { 5 } { 13 } }$
C) $y ^ { \frac { 5 } { 13 } }$
D) $22 y ^ { 13 }$
E) $4 y ^ { \frac { 13 } { 5 } }$

Question 56

Simplify the expression. $27 ^ { \frac { 1 } { 3 } }$

A) $\frac { 1 } { 3 }$
B) $9$
C) $\frac { 1 } { 32 }$
D) $2$
E) $3$

Question 57

Perform the indicated operation and express your answer in simplest radical form. $\sqrt { 5 } \cdot \sqrt [ 3 ] { 5 }$

A) $\sqrt [ 5 ] { 125 }$
B) $\sqrt [ 5 ] { 3,125 }$
C) $\sqrt [ 6 ] { 25 }$
D) $\sqrt [ 6 ] { 5 }$
E) $\sqrt [ 6 ] { 3,125 }$

Question 58

Simplify the expression. $\left( \frac { 25 } { 36 } \right) ^ { \frac { 3 } { 2 } }$

A) $\frac { 5 } { 6 }$
B) $\frac { 625 } { 1,296 }$
C) $\frac { 125 } { 216 }$
D) $\frac { 216 } { 125 }$
E) $\frac { 126 } { 217 }$

Question 59

Solve the equation. Write all solutions and then indicate which of those solutions are extraneous. $\sqrt [ 3 ] { x ^ { 3 } + 1,854 } - 6 = x$

A) $x = 7 , x = - 13$ is extraneous
B) $x = 6 , x = - 13$ is extraneous
C) $x = 6 , x = - 13$
D) $x = 7 , x = - 5$
E) $x = 7 , x = - 13$

Question 60

Solve the equation. Check all solutions. $\sqrt { x - 6 } - 4 = 5$

A)85
B)64
C)87
D)76
E)no solution

Question 61

Write the number 330,000 in scientific notation.

A) $33 \times 10 ^ { 5 }$
B) $33 \times 10 ^ { 6 }$
C) $3.3 \times 10 ^ { 4 }$
D) $33 \times 10 ^ { 4 }$
E) $3.3 \times 10 ^ { 5 }$

Question 62

Write the number 0.00061 in scientific notation.

A) $61 \times 10 ^ { - 4 }$
B) $6.1 \times 10 ^ { - 6 }$
C) $61 \times 10 ^ { - 5 }$
D) $6.1 \times 10 ^ { - 4 }$
E) $6.1 \times 10 ^ { - 5 }$

Question 63

The distance from earth to a certain star outside our solar system is 25,800,000,000,000 miles. Express this number in scientific notation.

A) $2.58 \times 10 ^ { - 13 }$ miles
B) $25.8 \times 10 ^ { - 12 }$ miles
C) $2.58 \times 10 ^ { 13 }$ miles
D) $2.58 \times 10 ^ { 12 }$ miles
E) $25.8 \times 10 ^ { 12 }$ miles

Question 64

Write the number $0.07 \times 10 ^ { 5 }$ in standard notation.

A)7,000,000
B)7
C)700
D)7,000
E)70,000

Question 65

Write the number $511 \times 10 ^ { - 2 }$ in standard notation.

A)5.11
B)51.1
C)5,110
D)0.00511
E)51,100

Question 66

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (0.006)(110,000)

A)6600
B)660
C)11.6
D)7100
E)710

Question 67

Write the number $48.3 \times 10 ^ { 3 }$ in scientific notation.

A) $483 \times 10 ^ { 2 }$
B)48,300
C) $4.83 \times 10 ^ { 3 }$
D) $4.83 \times 10 ^ { 4 }$
E) $4.83 \times 10 ^ { 5 }$

Question 68

Use scientific notation and the rules for exponents to simplify the following expression. Express your answer in standard notation. $\left( 7.6 \times 10 ^ { 2 } \right) \left( 2.6 \times 10 ^ { 3 } \right)$

A)1,976,000
B)197,600
C)1,976,000,000
D)197,600,000
E)19,760,000

Question 69

The distance between the Sun and Mercury is approximately $3.6 \times 10 ^ { 7 }$ miles. Use scientific notation to express this distance in feet. ( Hint: 5,280 feet = 1 mile.)

A) $190.08 \times 10 ^ { 9 }$ ft
B) $0.19008 \times 10 ^ { 12 }$ ft
C) $1.9008 \times 10 ^ { 12 }$ ft
D) $1.9008 \times 10 ^ { 11 }$ ft
E) $19.008 \times 10 ^ { 10 }$ ft