Question 1

Use rational exponents to simplify. Assume that all variables represent positive real numbers.
-$\sqrt [ 6 ] { 216 }$

Accepted Answer

A)  $6 \sqrt { 6 }$ 
B)  $\sqrt [ 3 ] { 6 }$ 
C)  $\sqrt { 6 }$ 
D)  $\frac { 1 } { 36 }$ 
A)  $6 \sqrt { 6 }$ 
B)  $\sqrt [ 3 ] { 6 }$ 
C)  $\sqrt { 6 }$ 
D)  $\frac { 1 } { 36 }$ C

Question 2

Solve.
-$$\sqrt { 5 x - 9 } = 3 - x$$

Accepted Answer

A)  9 
B)  2,9 
C)  2 
D)  $\varnothing$ 
A)  9 
B)  2,9 
C)  2 
D)  $\varnothing$ C

Question 3

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { 3 } { \sqrt { 6 } - 4 }$

Accepted Answer

A)  $- \frac { 3 \sqrt { 6 } + 12 } { 10 }$ 
B)  $\frac { 3 \sqrt { 6 } + 12 } { 10 }$ 
C)  $- \frac { 3 \sqrt { 6 } - 12 } { 10 }$ 
D)  $\frac { 3 \sqrt { 6 } - 12 } { 10 }$ 
A)  $- \frac { 3 \sqrt { 6 } + 12 } { 10 }$ 
B)  $\frac { 3 \sqrt { 6 } + 12 } { 10 }$ 
C)  $- \frac { 3 \sqrt { 6 } - 12 } { 10 }$ 
D)  $\frac { 3 \sqrt { 6 } - 12 } { 10 }$ A

Question 4

Use the properties of exponents to simplify. Write with positive exponents.
-$$x ^ { 7 / 8 } \cdot x ^ { 1 / 8 }$$

Accepted Answer

A)  $x ^ { 7 / 8 }$ 
B)  $\frac { 1 } { x }$ 
C)  $x ^ { 7 / 64 }$ 
D)  $x$ 
A)  $x ^ { 7 / 8 }$ 
B)  $\frac { 1 } { x }$ 
C)  $x ^ { 7 / 64 }$ 
D)  $x$

Question 5

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt { x - 5 } + 2 ) ^ { 2 }$

Accepted Answer

A)  $x + 4 \sqrt { x - 5 } + 9$ 
B)  $x + 4 \sqrt { x - 5 } - 1$ 
C)  $x + 4 \sqrt { x - 5 } + 49$ 
D)  $x + 4 \sqrt { x - 5 } + 4$ 
A)  $x + 4 \sqrt { x - 5 } + 9$ 
B)  $x + 4 \sqrt { x - 5 } - 1$ 
C)  $x + 4 \sqrt { x - 5 } + 49$ 
D)  $x + 4 \sqrt { x - 5 } + 4$

Question 6

Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 7 - 3 i } { 4 + 8 i }$

Accepted Answer

A)  $\frac { 1 } { 20 } - \frac { 17 } { 20 } \mathrm { i }$ 
B)  $\frac { 13 } { 5 } - \frac { 11 } { 5 } \mathrm { i }$ 
C)  $- \frac { 1 } { 48 } + \frac { 17 } { 48 } \mathrm { i }$ 
D)  $- \frac { 13 } { 12 } + \frac { 17 } { 48 } \mathrm { i }$ 
A)  $\frac { 1 } { 20 } - \frac { 17 } { 20 } \mathrm { i }$ 
B)  $\frac { 13 } { 5 } - \frac { 11 } { 5 } \mathrm { i }$ 
C)  $- \frac { 1 } { 48 } + \frac { 17 } { 48 } \mathrm { i }$ 
D)  $- \frac { 13 } { 12 } + \frac { 17 } { 48 } \mathrm { i }$

Question 7

Find the distance between the pair of points.
-$( 6,6 )$ and $( - 4 , - 1 )$

Accepted Answer

A)  149 units 
B)  $\sqrt { 149 }$ units 
C)  70 units 
D)  $\sqrt { 51 }$ units 
A)  149 units 
B)  $\sqrt { 149 }$ units 
C)  70 units 
D)  $\sqrt { 51 }$ units

Question 8

Solve.
-$$- \sqrt { 5 x + 5 } = - 8$$

Accepted Answer

A)  $\frac { 5 } { 59 }$ 
B)  295 
C)  $\frac { 59 } { 5 }$ 
D)  $\varnothing$ 
A)  $\frac { 5 } { 59 }$ 
B)  295 
C)  $\frac { 59 } { 5 }$ 
D)  $\varnothing$

Question 9

Solve.
-$$\sqrt { x - 5 } = 9$$

Accepted Answer

A)  81 
B)  196 
C)  86 
D)  76 
A)  81 
B)  196 
C)  86 
D)  76

Question 10

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt { 2 x } - 3 \sqrt { 7 } ) ( \sqrt { 2 x } - 3 \sqrt { 3 } )$

Accepted Answer

A)  $2 x - 3 \sqrt { 6 x } - 3 \sqrt { 14 x } + 9 \sqrt { 7 }$ 
B)  $2 x - 3 \sqrt { 42 x } + 9 \sqrt { 21 }$ 
C)  $4 x ^ { 2 } - 3 \sqrt { 6 x } - 3 \sqrt { 14 x } + 9 \sqrt { 21 }$ 
D)  $2 x - 3 \sqrt { 6 x } - 3 \sqrt { 14 x } + 9 \sqrt { 21 }$ 
A)  $2 x - 3 \sqrt { 6 x } - 3 \sqrt { 14 x } + 9 \sqrt { 7 }$ 
B)  $2 x - 3 \sqrt { 42 x } + 9 \sqrt { 21 }$ 
C)  $4 x ^ { 2 } - 3 \sqrt { 6 x } - 3 \sqrt { 14 x } + 9 \sqrt { 21 }$ 
D)  $2 x - 3 \sqrt { 6 x } - 3 \sqrt { 14 x } + 9 \sqrt { 21 }$

Question 11

Evaluate.
-If $f ( x ) = \sqrt { 2 x - 2 }$, find the value of $f ( 3 )$

Accepted Answer

A)  4 
B)  $\sqrt { 6 }$ 
C)  2 
D)  6 
A)  4 
B)  $\sqrt { 6 }$ 
C)  2 
D)  6

Question 12

Fill in the blank with one of the words or phrases listed below.

-In the notation $\sqrt [ n ] { a } , n$ is called the ـــــــــــand $\mathrm { a }$ is called theــــــــــــــــــــــــ

Accepted Answer

A)  index; radicand 
B)  conjugate; radicand 
C)  radicand; index 
D)  index; conjugate 
A)  index; radicand 
B)  conjugate; radicand 
C)  radicand; index 
D)  index; conjugate

Question 13

Use the quotient rule to divide and simplify.
-$$\sqrt { \frac { 12 x ^ { 2 } y } { 49 } }$$

Accepted Answer

A)  $\frac { 2 \times \sqrt { 3 y } } { 7 }$ 
B)  $\times \sqrt { \frac { 12 y } { 7 } }$ 
C)  $\frac { 2 \sqrt { 3 x ^ { 2 } y } } { 7 }$ 
D)  $4 x \sqrt { 3 y }$ 
A)  $\frac { 2 \times \sqrt { 3 y } } { 7 }$ 
B)  $\times \sqrt { \frac { 12 y } { 7 } }$ 
C)  $\frac { 2 \sqrt { 3 x ^ { 2 } y } } { 7 }$ 
D)  $4 x \sqrt { 3 y }$

Question 14

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { 11 } } { \sqrt { 5 } }$

Accepted Answer

A)  $\sqrt { 11 }$ 
B)  $\sqrt { 55 }$ 
C)  $\frac { \sqrt { 55 } } { 25 }$ 
D)  $\frac { \sqrt { 55 } } { 5 }$ 
A)  $\sqrt { 11 }$ 
B)  $\sqrt { 55 }$ 
C)  $\frac { \sqrt { 55 } } { 25 }$ 
D)  $\frac { \sqrt { 55 } } { 5 }$

Question 15

Simplify. Assume that all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 343 x ^ { 4 } y ^ { 5 } }$$

Accepted Answer

A)  $3 x y \sqrt [ 3 ] { x y ^ { 2 } }$ 
B)  $7 x y \sqrt { x y ^ { 2 } }$ 
C)  $7 x y \sqrt [ 3 ] { x y ^ { 2 } }$ 
D)  $7x y \sqrt [ 3 ] { x y }$ 
A)  $3 x y \sqrt [ 3 ] { x y ^ { 2 } }$ 
B)  $7 x y \sqrt { x y ^ { 2 } }$ 
C)  $7 x y \sqrt [ 3 ] { x y ^ { 2 } }$ 
D)  $7x y \sqrt [ 3 ] { x y }$

Question 16

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt { 300 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Accepted Answer

A)  $10 q ^ { 4 } \sqrt { 3 k ^ { 7 } }$ 
B)  $10 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 3 }$ 
C)  $10 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 3 \mathrm { k } }$ 
D)  $10 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } \sqrt { 3 \mathrm { k } }$ 
A)  $10 q ^ { 4 } \sqrt { 3 k ^ { 7 } }$ 
B)  $10 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 3 }$ 
C)  $10 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 3 \mathrm { k } }$ 
D)  $10 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } \sqrt { 3 \mathrm { k } }$

Question 17

Find the power of i.
-$( 3 i ) ^ { 4 }$

Accepted Answer

A)  $81 \mathrm { i }$ 
B)  $- 81 \mathrm { i }$ 
C)  $- 81$ 
D)  81 
A)  $81 \mathrm { i }$ 
B)  $- 81 \mathrm { i }$ 
C)  $- 81$ 
D)  81

Question 18

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$$( \sqrt [ 3 ] { x } + - 6 ) ( \sqrt [ 3 ] { x } + 4 \sqrt { x } - 4 )$$

Accepted Answer

A)  $4 \sqrt [ 6 ] { x ^ { 5 } } - 9 \sqrt [ 3 ] { x } - 24 \sqrt { x } + 24$ 
B)  $4 \sqrt [ 6 ] { x ^ { 5 } } + \sqrt [ 3 ] { x ^ { 2 } } - 10 \sqrt [ 3 ] { x } - 24 \sqrt { x } + 24$ 
C)  $\sqrt [ 3 ] { x ^ { 2 } } - 10 \sqrt [ 3 ] { x } - 24 \sqrt { x } + 4 \sqrt [ 6 ] { x } + 24$ 
D)  $- 10 \sqrt [ 3 ] { x } - 24 \sqrt { x } + 4 \sqrt [ 6 ] { x } + \sqrt [ 9 ] { x } + 24$ 
A)  $4 \sqrt [ 6 ] { x ^ { 5 } } - 9 \sqrt [ 3 ] { x } - 24 \sqrt { x } + 24$ 
B)  $4 \sqrt [ 6 ] { x ^ { 5 } } + \sqrt [ 3 ] { x ^ { 2 } } - 10 \sqrt [ 3 ] { x } - 24 \sqrt { x } + 24$ 
C)  $\sqrt [ 3 ] { x ^ { 2 } } - 10 \sqrt [ 3 ] { x } - 24 \sqrt { x } + 4 \sqrt [ 6 ] { x } + 24$ 
D)  $- 10 \sqrt [ 3 ] { x } - 24 \sqrt { x } + 4 \sqrt [ 6 ] { x } + \sqrt [ 9 ] { x } + 24$

Question 19

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt { \frac { x } { 7 } } \cdot \sqrt { \frac { y } { 3 } }$

Accepted Answer

A)  $\sqrt { \frac { 3 x } { 7 y } }$ 
B)  $\frac { x y } { 21 }$ 
C)  $\sqrt { \frac { x y } { 21 } }$ 
D)  $\sqrt { \frac { 3 x + 7 y } { 21 } }$ 
A)  $\sqrt { \frac { 3 x } { 7 y } }$ 
B)  $\frac { x y } { 21 }$ 
C)  $\sqrt { \frac { x y } { 21 } }$ 
D)  $\sqrt { \frac { 3 x + 7 y } { 21 } }$

Question 20

Add or subtract. Assume all variables represent positive real numbers.
-$$6 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$$

Accepted Answer

A)  $6 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$ 
B)  $2 \sqrt [ 3 ] { 2 }$ 
C)  $10 \sqrt [ 3 ] { 2 }$ 
D)  $- 10 \sqrt [ 3 ] { 2 }$ 
A)  $6 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$ 
B)  $2 \sqrt [ 3 ] { 2 }$ 
C)  $10 \sqrt [ 3 ] { 2 }$ 
D)  $- 10 \sqrt [ 3 ] { 2 }$

Use rational exponents to simplify. Assume that all variables represent positive real numbers. - $\sqrt [ 6 ] { 216 }$

Solve. - $\sqrt { 5 x - 9 } = 3 - x$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { 3 } { \sqrt { 6 } - 4 }$

Use the properties of exponents to simplify. Write with positive exponents. - $x ^ { 7 / 8 } \cdot x ^ { 1 / 8 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt { x - 5 } + 2 ) ^ { 2 }$

Perform the indicated operation. Write the result in the form a + bi. - $\frac { 7 - 3 i } { 4 + 8 i }$

Find the distance between the pair of points. - $( 6,6 )$ and $( - 4 , - 1 )$

Solve. - $- \sqrt { 5 x + 5 } = - 8$

Solve. - $\sqrt { x - 5 } = 9$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt { 2 x } - 3 \sqrt { 7 } ) ( \sqrt { 2 x } - 3 \sqrt { 3 } )$

Evaluate. -If $f ( x ) = \sqrt { 2 x - 2 }$ , find the value of $f ( 3 )$

Use the quotient rule to divide and simplify. - $\sqrt { \frac { 12 x ^ { 2 } y } { 49 } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { \sqrt { 11 } } { \sqrt { 5 } }$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt [ 3 ] { 343 x ^ { 4 } y ^ { 5 } }$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt { 300 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Find the power of i. - $( 3 i ) ^ { 4 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt [ 3 ] { x } + - 6 ) ( \sqrt [ 3 ] { x } + 4 \sqrt { x } - 4 )$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt { \frac { x } { 7 } } \cdot \sqrt { \frac { y } { 3 } }$

Add or subtract. Assume all variables represent positive real numbers. - $6 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

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Filters

Exam 7: Rational Exponents, Radicals, and Complex Numbers

Use rational exponents to simplify. Assume that all variables represent positive real numbers. - 2166\sqrt [ 6 ] { 216 }6216​

Solve. - 5x−9=3−x\sqrt { 5 x - 9 } = 3 - x5x−9​=3−x

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 36−4\frac { 3 } { \sqrt { 6 } - 4 }6​−43​

Use the properties of exponents to simplify. Write with positive exponents. - x7/8⋅x1/8x ^ { 7 / 8 } \cdot x ^ { 1 / 8 }x7/8⋅x1/8

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (x−5+2)2( \sqrt { x - 5 } + 2 ) ^ { 2 }(x−5​+2)2

Perform the indicated operation. Write the result in the form a + bi. - 7−3i4+8i\frac { 7 - 3 i } { 4 + 8 i }4+8i7−3i​

Find the distance between the pair of points. - (6,6)( 6,6 )(6,6) and (−4,−1)( - 4 , - 1 )(−4,−1)

Solve. - −5x+5=−8- \sqrt { 5 x + 5 } = - 8−5x+5​=−8

Solve. - x−5=9\sqrt { x - 5 } = 9x−5​=9

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (2x−37)(2x−33)( \sqrt { 2 x } - 3 \sqrt { 7 } ) ( \sqrt { 2 x } - 3 \sqrt { 3 } )(2x​−37​)(2x​−33​)

Evaluate. -If f(x)=2x−2f ( x ) = \sqrt { 2 x - 2 }f(x)=2x−2​ , find the value of f(3)f ( 3 )f(3)

Fill in the blank with one of the words or phrases listed below. -In the notation an,n\sqrt [ n ] { a } , nna​,n is called the ـــــــــــand a\mathrm { a }a is called theــــــــــــــــــــــــ

Use the quotient rule to divide and simplify. - 12x2y49\sqrt { \frac { 12 x ^ { 2 } y } { 49 } }4912x2y​​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 115\frac { \sqrt { 11 } } { \sqrt { 5 } }5​11​​

Simplify. Assume that all variables represent positive real numbers. - 343x4y53\sqrt [ 3 ] { 343 x ^ { 4 } y ^ { 5 } }3343x4y5​

Simplify. Assume that all variables represent positive real numbers. - 300k7q8\sqrt { 300 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }300k7q8​

Find the power of i. - (3i)4( 3 i ) ^ { 4 }(3i)4

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (x3+−6)(x3+4x−4)( \sqrt [ 3 ] { x } + - 6 ) ( \sqrt [ 3 ] { x } + 4 \sqrt { x } - 4 )(3x​+−6)(3x​+4x​−4)

Use the product rule to multiply. Assume all variables represent positive real numbers. - x7⋅y3\sqrt { \frac { x } { 7 } } \cdot \sqrt { \frac { y } { 3 } }7x​​⋅3y​​

Add or subtract. Assume all variables represent positive real numbers. - 623−412836 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }632​−43128​