Question 1

Perform the operation and simplify, expressing answer with a positive exponent in lowest terms:  x7/8x1/8\frac { x ^ { 7 / 8 } } { x ^ { 1 / 8 } }x1/8x7/8​

Accepted Answer

A)    x7x 7x7 
B)    x3/4x ^ { 3 / 4 }x3/4 
C)    x4/3x ^ { 4 / 3 }x4/3 
D)    x6x 6x6E) A) and B)
F) A) and C) B

Question 2

Write in radical notation: the seventh root of the square of x

Accepted Answer

A)    x7\sqrt { x ^ { 7 } }x7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    x27\sqrt [ 7 ] { x ^ { 2 } }7x2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    x2/7x ^ { 2 / 7 }x2/7 
D)    x7\sqrt [ 7 ] { x }7xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) B) and D)
F) A) and B)

Question 3

Write  3x\sqrt { 3 x }3x​  in rational exponential form.

Accepted Answer

A)    (3x) 12( 3 x )  ^ { \frac { 1 } { 2 } }(3x) 21​  
B)    3x123 x ^ { \frac { 1 } { 2 } }3x21​  
C)    (3x) 2( 3 x )  ^ { 2 }(3x) 2  
D)    3x23 x ^ { 2 }3x2  E) A) and C)
F) C) and D)

Question 4

Write the fourth root of the cube of x using rational exponent notation.

Accepted Answer

The answer of Write the fourth root of the cube...

Question 5

Write   x27x ^ { \frac { 2 } { 7 } }x72​   in radical form.

Accepted Answer

A)    x27\sqrt [ 7 ] { x ^ { 2 } }7x2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    x77\sqrt [ 7 ] { x ^ { 7 } }7x7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    x\sqrt { x }xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    x7\sqrt [ 7 ] { x }7xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​   E) A) and B)
F) All of the above

Question 6

Simplify:  12y10\sqrt { 12 y ^ { 10 } }12y10​

Accepted Answer

A)    2y53y2 y ^ { 5 } \sqrt { 3 y }2y53yc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    23y52 \sqrt { 3 y ^ { 5 } }23y5c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​ 
C)    2y532 y ^ { 5 } \sqrt { 3 }2y53c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    3y523 y ^ { 5 } \sqrt { 2 }3y52c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​   E) C) and D)
F) A) and B)

Question 7

Perform the indicated operation and write the answer with positive exponent in lowest terms:
 $\frac { ( x ) ^ { 4 / 7 } } { ( x ) ^ { 3 / 7 } }$

Accepted Answer

$( x ) ^ { 1 / 7 }$

Question 8

Evaluate the expression:  (49) −12\left( \frac { 4 } { 9 } \right)  ^ { - \frac { 1 } { 2 } }(94​) −21​

Accepted Answer

A)    =−23= -\frac { 2 } { 3 }=−32​ 
B)    32\frac { 3 } { 2 }23​ 
C)   =−29 =- \frac { 2 } { 9 }=−92​ D  8116\frac { 81 } { 16 }1681​D) A) and C)
E) All of the above

Question 9

Use the calculator to find the approximate value of the root  361/336 ^ { 1 / 3 }361/3

Accepted Answer

A)  6
B)  2.449489743
C)  3.301927249
D)  12 E) A) and B)
F) A) and C)

Question 10

On the number line below, locate
 $\sqrt { 2 }$

Accepted Answer

The answer of On the number line below, locate
 \(\sqrt...

Question 11

Divide and simplify:

Accepted Answer

A)    a16a ^ { \frac { 1 } { 6 } }a61​ 
B)    a6a ^ { 6 }a6 
C)    a43a ^ { \frac { 4 } { 3 } }a34​ 
D)    a13a ^ { \frac { 1 } { 3 } }a31​   E) None of the above
F) A) and B)

Question 12

Perform the indicated operation and write the answer with positive exponents in lowest terms:
 $( a ) ^ { 3 / 7 } \cdot ( a ) ^ { - 2 / 7 }$

Accepted Answer

$( a ) ^ { 1 / 7 }$

Question 13

Simplify the following:
 $[ \sqrt { 2 } ] 2$

Accepted Answer

The answer of Simplify the following:
 \([ \sqrt { 2...

Question 14

Perform the indicated operation and write the answer with positive exponents in simplest form:
 $\left( 64 x^{ 1 / 3} y ^ { 9 } \right) ^ { 1 / 3 }$

Accepted Answer

The answer of Perform the indicated operation and write the...

Question 15

Raise the term to the indicated power and simplify:  (a23b14) 6\left( a ^ { \frac { 2 } { 3 } } b ^ { \frac { 1 } { 4 } } \right)  ^ { 6 }(a32​b41​) 6

Accepted Answer

A)    a203,b254 a^ \frac{20}{3}, b^ \frac{25}{4}a320​,b425​ 
B)    a4b32a ^ { 4 } b ^ { \frac { 3 } { 2 } }a4b23​ 
C)    ab112a b ^ { \frac { 11 } { 2 } }ab211​ 
D)    a23b14a ^ { \frac { 2 } { 3 } } b^\frac { 1 } { 4 }a32​b41​    E) B) and D)
F) B) and C)

Question 16

Write with fractional exponents:
 $\sqrt [ 5 ] { x }$

Accepted Answer

The answer of Write with fractional exponents:
 \(\sqrt [ 5...

Question 17

Write the square of the seventh root of x in rational exponent form.

Accepted Answer

A)    (x7) 2( \sqrt [ 7 ] { x } )  ^ { 2 }(7xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​) 2 
B)    x12x ^ { \frac { 1 } { 2 } }x21​ 
C)    x72x ^ { \frac { 7 } { 2 } }x27​ 
D)    x27x ^ { \frac { 2 } { 7 } }x72​E) A) and B)
F) A) and C)

Question 18

Determine the two whole numbers between which lies.  401/240 ^ { 1 / 2 }401/2

Accepted Answer

A)  6 and 7
B)  4 and 5
C)  7 and 8
D)  5 and 6 E) None of the above
F) A) and C)

Question 19

Raise to indicated power and simplify:  (2x34y2) 4\left( 2 x ^ { \frac { 3 } { 4 } } y ^ { 2 } \right)  ^ { 4 }(2x43​y2) 4

Accepted Answer

A)    16x3y816 x^ 3 y 816x3y8  
B)    16x194y616 x ^ { \frac { 19 } { 4 } } y ^ { 6 }16x419​y6  
C)    2x3y22 x ^3 y^ 22x3y2  
D)    8x3y88 x ^ { 3 } y ^ { 8 }8x3y8  E) A) and B)
F) None of the above

Question 20

Write the cube root of x in radical form.

Accepted Answer

A)    x3\sqrt { x ^ { 3 } }x3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    x3\sqrt [ 3 ] { x }3xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    x3x ^ { 3 }x3 
D)    x13x ^ { \frac { 1 } { 3 } }x31​E) A) and B)
F) B) and C)

Exam 12: Roots and Radicals

Perform the operation and simplify, expressing answer with a positive exponent in lowest terms: x7/8x1/8\frac { x ^ { 7 / 8 } } { x ^ { 1 / 8 } }x1/8x7/8​

Correct AnswerverifiedB

Write in radical notation: the seventh root of the square of x

Correct AnswerverifiedShow Answer

Write 3x\sqrt { 3 x }3x​ in rational exponential form.

Correct AnswerverifiedShow Answer

Write the fourth root of the cube of x using rational exponent notation.

Correct AnswerverifiedShow Answer

Write x27x ^ { \frac { 2 } { 7 } }x72​ in radical form.

Correct AnswerverifiedShow Answer

Simplify: 12y10\sqrt { 12 y ^ { 10 } }12y10​

Correct AnswerverifiedShow Answer

Perform the indicated operation and write the answer with positive exponent in lowest terms: (x)4/7(x)3/7\frac { ( x ) ^ { 4 / 7 } } { ( x ) ^ { 3 / 7 } }(x)3/7(x)4/7​

Correct Answerverified\(( x ) ^ { 1 / 7 }\)

Evaluate the expression: (49) −12\left( \frac { 4 } { 9 } \right) ^ { - \frac { 1 } { 2 } }(94​) −21​

Correct AnswerverifiedShow Answer

Use the calculator to find the approximate value of the root 361/336 ^ { 1 / 3 }361/3

Correct AnswerverifiedShow Answer

On the number line below, locate 2\sqrt { 2 }2​

Correct AnswerverifiedShow Answer

Divide and simplify:

Correct AnswerverifiedShow Answer

Perform the indicated operation and write the answer with positive exponents in lowest terms: (a)3/7⋅(a)−2/7( a ) ^ { 3 / 7 } \cdot ( a ) ^ { - 2 / 7 }(a)3/7⋅(a)−2/7

Correct Answerverified\(( a ) ^ { 1 / 7 }\)

Simplify the following: [2]2[ \sqrt { 2 } ] 2[2​]2

Correct AnswerverifiedShow Answer

Perform the indicated operation and write the answer with positive exponents in simplest form: (64x1/3y9)1/3\left( 64 x^{ 1 / 3} y ^ { 9 } \right) ^ { 1 / 3 }(64x1/3y9)1/3

Correct AnswerverifiedShow Answer

Raise the term to the indicated power and simplify: (a23b14) 6\left( a ^ { \frac { 2 } { 3 } } b ^ { \frac { 1 } { 4 } } \right) ^ { 6 }(a32​b41​) 6

Correct AnswerverifiedShow Answer

Write with fractional exponents: x5\sqrt [ 5 ] { x }5x​

Correct AnswerverifiedShow Answer

Write the square of the seventh root of x in rational exponent form.

Correct AnswerverifiedShow Answer

Determine the two whole numbers between which lies. 401/240 ^ { 1 / 2 }401/2

Correct AnswerverifiedShow Answer

Raise to indicated power and simplify: (2x34y2) 4\left( 2 x ^ { \frac { 3 } { 4 } } y ^ { 2 } \right) ^ { 4 }(2x43​y2) 4

Correct AnswerverifiedShow Answer

Write the cube root of x in radical form.

Correct AnswerverifiedShow Answer

Perform the operation and simplify, expressing answer with a positive exponent in lowest terms: $\frac { x ^ { 7 / 8 } } { x ^ { 1 / 8 } }$

Correct Answer
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B

Correct Answer
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Write $\sqrt { 3 x }$ in rational exponential form.

Correct Answer
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Correct Answer
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Write $x ^ { \frac { 2 } { 7 } }$ in radical form.

Correct Answer
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Simplify: $\sqrt { 12 y ^ { 10 } }$

Correct Answer
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Perform the indicated operation and write the answer with positive exponent in lowest terms: $\frac { ( x ) ^ { 4 / 7 } } { ( x ) ^ { 3 / 7 } }$

Correct Answer
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\(( x ) ^ { 1 / 7 }\)

Evaluate the expression: $\left( \frac { 4 } { 9 } \right) ^ { - \frac { 1 } { 2 } }$

Correct Answer
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Use the calculator to find the approximate value of the root $36 ^ { 1 / 3 }$

Correct Answer
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On the number line below, locate $\sqrt { 2 }$ $On the number line below, locate \sqrt { 2 }$

Correct Answer
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Divide and simplify: $Divide and simplify: A) a ^ { \frac { 1 } { 6 } } B) a ^ { 6 } C) a ^ { \frac { 4 } { 3 } } D) a ^ { \frac { 1 } { 3 } }$

Correct Answer
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Perform the indicated operation and write the answer with positive exponents in lowest terms: $( a ) ^ { 3 / 7 } \cdot ( a ) ^ { - 2 / 7 }$

Correct Answer
verified
\(( a ) ^ { 1 / 7 }\)

Simplify the following: $[ \sqrt { 2 } ] 2$

Correct Answer
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Perform the indicated operation and write the answer with positive exponents in simplest form: $\left( 64 x^{ 1 / 3} y ^ { 9 } \right) ^ { 1 / 3 }$

Correct Answer
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Raise the term to the indicated power and simplify: $\left( a ^ { \frac { 2 } { 3 } } b ^ { \frac { 1 } { 4 } } \right) ^ { 6 }$

Correct Answer
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Write with fractional exponents: $\sqrt [ 5 ] { x }$

Correct Answer
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Correct Answer
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Determine the two whole numbers between which lies. $40 ^ { 1 / 2 }$

Correct Answer
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Raise to indicated power and simplify: $\left( 2 x ^ { \frac { 3 } { 4 } } y ^ { 2 } \right) ^ { 4 }$

Correct Answer
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Correct Answer
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