Question 1

Perform the indicated operation. Write the result in the form a + bi.
-$5 \mathrm { i } + ( - 6 - \mathrm { i } )$

Accepted Answer

A)  $- 6 + 4 i$ 
B)  $6 - 6 i$ 
C)  $6 - 4 i$ 
D)  $- 6 + 6 i$ 
A)  $- 6 + 4 i$ 
B)  $6 - 6 i$ 
C)  $6 - 4 i$ 
D)  $- 6 + 6 i$

Question 2

Perform the indicated operation and simplify. Write the result in the form a + bi.
-$\sqrt { - 148 }$

Accepted Answer

A)  $- 2 i \sqrt { 37 }$ 
B)  $2 \sqrt { 37 }$ 
C)  $2 \mathrm { i } \sqrt { 37 }$ 
D)  $- 2 \sqrt { 37 }$ 
A)  $- 2 i \sqrt { 37 }$ 
B)  $2 \sqrt { 37 }$ 
C)  $2 \mathrm { i } \sqrt { 37 }$ 
D)  $- 2 \sqrt { 37 }$

Question 3

Use the properties of exponents to simplify. Write with positive exponents.
-$\frac { x ^ { - 1 / 2 } y ^ { 3 / 8 } } { \left( x ^ { 4 } y ^ { - 5 } \right) ^ { - 1 / 2 } }$

Accepted Answer

A)  $\frac { y ^ { 17 / 8 } } { x ^ { 3 / 2 } }$ 
B)  $\frac { x ^ { 3 / 2 } } { y ^ { 17 / 8 } }$ 
C)  $x ^ { 3 / 2 } y ^ { 17 / 8 }$ 
D)  $- \frac { x ^ { 3 / 2 } } { y ^ { 17 / 8 } }$ 
A)  $\frac { y ^ { 17 / 8 } } { x ^ { 3 / 2 } }$ 
B)  $\frac { x ^ { 3 / 2 } } { y ^ { 17 / 8 } }$ 
C)  $x ^ { 3 / 2 } y ^ { 17 / 8 }$ 
D)  $- \frac { x ^ { 3 / 2 } } { y ^ { 17 / 8 } }$

Question 4

Use the properties of exponents to simplify. Write with positive exponents.
-$\frac { \left( - 5 x ^ { 3 / 7 } \right) ^ { 2 } } { x ^ { 4 / 5 } }$

Accepted Answer

A)  $- 5 x ^ { 58 / 35 }$ 
B)  $25 x ^ { 2 / 35 }$ 
C)  $25 x ^ { 58 / 35 }$ 
D)  $- 5 x ^ { 2 / 35 }$ 
A)  $- 5 x ^ { 58 / 35 }$ 
B)  $25 x ^ { 2 / 35 }$ 
C)  $25 x ^ { 58 / 35 }$ 
D)  $- 5 x ^ { 2 / 35 }$

Question 5

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\sqrt [ 4 ] { \frac { 81 } { 8 } }$

Accepted Answer

A)  $\frac { 3 \sqrt { 2 } } { 2 }$ 
B)  $\frac { 3 \sqrt { 8 } } { 8 }$ 
C)  $\frac { 3 \sqrt [ 4 ] { 2 } } { 2 }$ 
D)  $\frac { 3 \sqrt { 8 } } { 2 }$ 
A)  $\frac { 3 \sqrt { 2 } } { 2 }$ 
B)  $\frac { 3 \sqrt { 8 } } { 8 }$ 
C)  $\frac { 3 \sqrt [ 4 ] { 2 } } { 2 }$ 
D)  $\frac { 3 \sqrt { 8 } } { 2 }$

Question 6

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { 7 } { \sqrt [ 3 ] { 9 x ^ { 2 } } }$

Accepted Answer

A)  $\frac { 7 \sqrt [ 3 ] { 9 x ^ { 2 } } } { 9 x ^ { 2 } }$ 
B)  $\frac { 7 \sqrt { 3 x } } { 3 x }$ 
C)  $\frac { 7 \sqrt [ 3 ] { x } } { x }$ 
D)  $\frac { 7 \sqrt [ 3 ] { 3 x } } { 3 x }$ 
A)  $\frac { 7 \sqrt [ 3 ] { 9 x ^ { 2 } } } { 9 x ^ { 2 } }$ 
B)  $\frac { 7 \sqrt { 3 x } } { 3 x }$ 
C)  $\frac { 7 \sqrt [ 3 ] { x } } { x }$ 
D)  $\frac { 7 \sqrt [ 3 ] { 3 x } } { 3 x }$

Question 7

Perform the indicated operation and simplify. Write the result in the form a + bi.
-$$( 8 + 4 i ) ( 8 - 4 i )$$

Accepted Answer

A)  48 
B)  80 
C)  $64 - 16 i$ 
D)  $64 - 16 i ^ { 2 }$ 
A)  48 
B)  80 
C)  $64 - 16 i$ 
D)  $64 - 16 i ^ { 2 }$

Question 8

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

-Radicals with the same index and the same radicand are calledـــــــــــــــــــــــ

Accepted Answer

A)  like radicals 
B)  rationalizing 
C)  conjugate 
D)  radicand 
A)  like radicals 
B)  rationalizing 
C)  conjugate 
D)  radicand

Question 9

Solve.
-$$\sqrt { 2 x + 3 } = 1 + \sqrt { x + 1 }$$

Accepted Answer

A)  1,3 
B)  $- 3,1$ 
C)  $- 1,3$ 
D)  $\varnothing$ 
A)  1,3 
B)  $- 3,1$ 
C)  $- 1,3$ 
D)  $\varnothing$

Question 10

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive
exponents.
-$\sqrt { 28 }$

Accepted Answer

A)  $7 \sqrt { 2 }$ 
B)  $2 \sqrt { 7 }$ 
C)  5 
D)  14 
A)  $7 \sqrt { 2 }$ 
B)  $2 \sqrt { 7 }$ 
C)  5 
D)  14

Question 11

Find the root. Assume that all variables represent nonnegative real numbers.
-$- \sqrt [ 4 ] { 256 }$

Accepted Answer

A)  16 
B)  $6.233$ 
C)  $- 4$ 
D)  not real number 
A)  16 
B)  $6.233$ 
C)  $- 4$ 
D)  not real number

Question 12

Find the power of i.
-$\mathrm { i } ^ { - 15 }$

Accepted Answer

A)  $- \mathrm { i }$ 
B)  $\mathrm { i }$ 
C)  $- 1$ 
D)  1 
A)  $- \mathrm { i }$ 
B)  $\mathrm { i }$ 
C)  $- 1$ 
D)  1

Question 13

Perform the indicated operation. Write the result in the form a + bi.
-$( - 13 i ) ( - 9 i )$

Accepted Answer

A)  $- 117 \mathrm { i }$ 
B)  117 
C)  $- 117$ 
D)  $117 \mathrm { i }$ 
A)  $- 117 \mathrm { i }$ 
B)  117 
C)  $- 117$ 
D)  $117 \mathrm { i }$

Question 14

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

Accepted Answer

A)  $\sqrt [ 15 ] { 160 }$ 
B)  $\sqrt [ 15 ] { 4000 }$ 
C)  $\sqrt [ 5 ] { 10 }$ 
D)  $\sqrt [ 15 ] { 10 }$ 
A)  $\sqrt [ 15 ] { 160 }$ 
B)  $\sqrt [ 15 ] { 4000 }$ 
C)  $\sqrt [ 5 ] { 10 }$ 
D)  $\sqrt [ 15 ] { 10 }$

Question 15

Use the Pythagorean theorem to find the unknown side of the right triangle.
-

Accepted Answer

A)  25 
B)  $25 \sqrt { 5 }$ 
C)  $10 \sqrt { 5 }$ 
D)  $5 \sqrt { 5 }$ 
A)  25 
B)  $25 \sqrt { 5 }$ 
C)  $10 \sqrt { 5 }$ 
D)  $5 \sqrt { 5 }$

Question 16

Find the root. Assume that all variables represent nonnegative real numbers.
-$- \sqrt [ 4 ] { 256 x ^ { 12 } y ^ { 8 } }$

Accepted Answer

A)  $6.233 x ^ { 3 } y ^ { 2 }$ 
B)  $- 4 x ^ { 3 } y ^ { 2 }$ 
C)  $16 x ^ { 3 } y ^ { 2 }$ 
D)  not a real number 
A)  $6.233 x ^ { 3 } y ^ { 2 }$ 
B)  $- 4 x ^ { 3 } y ^ { 2 }$ 
C)  $16 x ^ { 3 } y ^ { 2 }$ 
D)  not a real number

Question 17

Add or subtract. Assume all variables represent positive real numbers.
-$\sqrt { 98 } - 3 \sqrt { 8 } + 9 \sqrt { 128 }$

Accepted Answer

A)  $- 73 \sqrt { 2 }$ 
B)  $- 8 \sqrt { 2 }$ 
C)  $- 4 \sqrt { 2 }$ 
D)  $73 \sqrt { 2 }$ 
A)  $- 73 \sqrt { 2 }$ 
B)  $- 8 \sqrt { 2 }$ 
C)  $- 4 \sqrt { 2 }$ 
D)  $73 \sqrt { 2 }$

Question 18

Use radical notation to write the expression. Simplify if possible.
-$$16 ^ { 1 / 4 }$$

Accepted Answer

A)  8 
B)  16 
C)  2 
D)  32 
A)  8 
B)  16 
C)  2 
D)  32

Question 19

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

-Theـــــــــــــــــــــــ formula is $\mathrm { d } = \sqrt { \left( \mathrm { x } _ { 2 } - \mathrm { x } _ { 1 } \right) ^ { 2 } + \left( \mathrm { y } _ { 2 } - \mathrm { y } _ { 1 } \right) ^ { 2 } }$.

Accepted Answer

A)  distance 
B)  midpoint 
C)  conjugate 
D)  index 
A)  distance 
B)  midpoint 
C)  conjugate 
D)  index

Question 20

Evaluate.
-If $f ( x ) = \sqrt [ 3 ] { x - 1 }$, find the value of $f ( - 1 )$

Accepted Answer

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

Perform the indicated operation. Write the result in the form a + bi. - $5 \mathrm { i } + ( - 6 - \mathrm { i } )$

Perform the indicated operation and simplify. Write the result in the form a + bi. - $\sqrt { - 148 }$

Use the properties of exponents to simplify. Write with positive exponents. - $\frac { x ^ { - 1 / 2 } y ^ { 3 / 8 } } { \left( x ^ { 4 } y ^ { - 5 } \right) ^ { - 1 / 2 } }$

Use the properties of exponents to simplify. Write with positive exponents. - $\frac { \left( - 5 x ^ { 3 / 7 } \right) ^ { 2 } } { x ^ { 4 / 5 } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 81 } { 8 } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { 7 } { \sqrt [ 3 ] { 9 x ^ { 2 } } }$

Perform the indicated operation and simplify. Write the result in the form a + bi. - $( 8 + 4 i ) ( 8 - 4 i )$

Fill in the blank with one of the words or phrases listed below. -Radicals with the same index and the same radicand are calledـــــــــــــــــــــــ

Solve. - $\sqrt { 2 x + 3 } = 1 + \sqrt { x + 1 }$

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - $\sqrt { 28 }$

Find the root. Assume that all variables represent nonnegative real numbers. - $- \sqrt [ 4 ] { 256 }$

Find the power of i. - $\mathrm { i } ^ { - 15 }$

Perform the indicated operation. Write the result in the form a + bi. - $( - 13 i ) ( - 9 i )$

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

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Find the root. Assume that all variables represent nonnegative real numbers. - $- \sqrt [ 4 ] { 256 x ^ { 12 } y ^ { 8 } }$

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { 98 } - 3 \sqrt { 8 } + 9 \sqrt { 128 }$

Use radical notation to write the expression. Simplify if possible. - $16 ^ { 1 / 4 }$

Evaluate. -If $f ( x ) = \sqrt [ 3 ] { x - 1 }$ , find the value of $f ( - 1 )$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 7: Rational Exponents, Radicals, and Complex Numbers

Perform the indicated operation. Write the result in the form a + bi. - 5i+(−6−i)5 \mathrm { i } + ( - 6 - \mathrm { i } )5i+(−6−i)

Perform the indicated operation and simplify. Write the result in the form a + bi. - −148\sqrt { - 148 }−148​

Use the properties of exponents to simplify. Write with positive exponents. - x−1/2y3/8(x4y−5)−1/2\frac { x ^ { - 1 / 2 } y ^ { 3 / 8 } } { \left( x ^ { 4 } y ^ { - 5 } \right) ^ { - 1 / 2 } }(x4y−5)−1/2x−1/2y3/8​

Use the properties of exponents to simplify. Write with positive exponents. - (−5x3/7)2x4/5\frac { \left( - 5 x ^ { 3 / 7 } \right) ^ { 2 } } { x ^ { 4 / 5 } }x4/5(−5x3/7)2​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 8184\sqrt [ 4 ] { \frac { 81 } { 8 } }4881​​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 79x23\frac { 7 } { \sqrt [ 3 ] { 9 x ^ { 2 } } }39x2​7​

Perform the indicated operation and simplify. Write the result in the form a + bi. - (8+4i)(8−4i)( 8 + 4 i ) ( 8 - 4 i )(8+4i)(8−4i)