Free Printable Intermediate Algebra Review

1.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

2.

Simplify:
(x - 9)(x - 7)

a)

x² - 2x - 63

b)

x² - 16x - 63

c)

x² - 2x + 63

d)

x² - 16x + 63

3.

Find the product:
(x + 5)(x - 4)

a)

x² + 9x + 20

b)

x² + 9x - 20

c)

x² + 1x - 20

d)

x² - 1x - 20

4.

Find the Product.
(2x + 3)(2x - 3)

a)

4x² - 9

b)

4x² + 9

c)

4x²- 12x - 9

d)

4x² + 12x - 9

5.

Find the Product.

(2n + 3)(2n + 1)

a)

4n² + 8n + 3

b)

4n² - 8n - 3

c)

4n² - 8n + 3

6.

Multiply:
(r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

7.

Find the Product.

(3p - 3)(p - 1)

a)

3p² + 6p + 3

b)

3p² - 6p + 3

c)

3p² - 6p - 3

d)

3p² + 6p - 3

8.

Find the product:
(x + 5)(x - 4)

a)

x² + 9x + 20

b)

x² + 9x - 20

c)

x² + 1x - 20

d)

x² - 1x - 20

9.

Find the product:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

10.

Simplify:
(x - 7)(x + 7)

a)

x² + 7x - 49

b)

x² - 7x + 49

c)

x² - 49

d)

x² + 49

11.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

12.

Find the product:
(x + 5)(x - 4)

a)

x² + 9x + 20

b)

x² + 9x - 20

c)

x² + 1x - 20

d)

x² - 1x - 20

13.

Find the product:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

14.

Simplify:
(x - 9)(x - 7)

a)

x² - 2x - 63

b)

x² - 16x - 63

c)

x² - 2x + 63

d)

x² - 16x + 63

15.

Multiply:
(r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

16.

Find the product:
(n - 5)(n - 1)

a)

n² - 5n + 5

b)

n² - 6n + 5

c)

n²+ 5

d)

n² + 6n + 5

17.

Find the product:
(x + 5)(x - 4)

a)

x² + 9x + 20

b)

x² + 9x - 20

c)

x² + 1x - 20

d)

x² - 1x - 20

18.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

19.

Simplify:
(x - 9)(x - 7)

a)

x² - 2x - 63

b)

x² - 16x - 63

c)

x² - 2x + 63

d)

x² - 16x + 63

20.

Find the product:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

21.

$\left(m+5\right)\left(m^2+4m-8\right)$

a)

$m^3+4m^2-8m+5m^2+20m-40$

b)

$m^2+40m+m^3$

c)

$m^3+9m^2+12m-40$

22.

$\left(x+3\right)\left(x^2+4x+7\right)$

a)

$x^3+7x^2+19x+21$

b)

$x^2+19x+7x+7$

c)

$x^3+x^2+19x+7$

23.

(3n-4)(3n-4)

a)

$9n^2-24n+16$

b)

$3n^2-4x+8$

c)

$n^2-24n+16$

24.

-5x⁶(3x² - 12x + 30)

a)

-15x⁸+ 60x⁷- 150x⁶

b)

15x⁸- 60x⁷- 150x⁶

c)

8x⁶- 17x + 35

d)

-8x⁶+ 17x - 35x²

25.

5x(2x³+6)

a)

10x⁴+30x

b)

10x³+30x

c)

7x⁴+11x

26.

Write the expanded (general) form of the product (x+3)(x+6).

a)

x²+18x+9

b)

x²+9x+18

c)

x²+18x+18

27.

(x-7)²

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

28.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

29.

The number under the radical sign or square root sign is called the ______.

a)

radical sign

b)

radicand

c)

factor

d)

exponent

30.

a)

x = 12

b)

x = 24

c)

x = 144

d)

x = 121

31.

a)

10

b)

8

c)

16

d)

4

32.

Solve

a)

8

b)

38

c)

34

d)

14

33.

a)

5

b)

4

c)

41

d)

82

34.

a)

2

b)

-2

c)

4

d)

-4

35.

Solve

a)

102

b)

12

c)

98

d)

7

36.

Solve the equation:

a)

A

b)

B

c)

C

d)

D

37.

Solve.

a)

8

b)

-8

c)

0

d)

no solution

38.

a)

1

b)

3

c)

224

d)

226

39.

a)

5

b)

33

c)

85

d)

21

40.

a)

20

b)

11

c)

4

d)

-2

41.

Solve the radical equation

a)

25

b)

50

c)

125

d)

5

42.

a)

9

b)

-9

c)

21

d)

-21

43.

a)

4

b)

-4

c)

2

d)

-2

44.

Solve

a)

-14

b)

14

c)

no solution

d)

28

45.

Solve

a)

20

b)

-4

c)

4

d)

-10

46.

a)

3

b)

-3

c)

2

d)

0

47.

a)

14

b)

-14

c)

6

d)

-6

48.

a)

3

b)

2

c)

-3

d)

-2

49.

Solve and check your solution(s).

a)

x = -2

b)

x = -2, 3

c)

x = -2, -3

d)

x = -3

50.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

51.

1 The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

52.

1 In the equation

y = x² +5x +7,

match each leading coefficient with its correct letter.

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

53.

1 What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

54.

2 For the function below, is the discriminant positive, negative, or zero?

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

55.

2 A function has a discriminant of 4.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

4

56.

2 A function has a discriminant of 0.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

5

57.

3 What is the discriminant of

-2x² − x − 1 = 0 ?

a)

76

b)

-7

c)

9

d)

none of these

58.

3 For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

59.

3 For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

60.

4 Determine the value of the discriminant and name the nature of the solution for the following:

x² + 2x - 63

Remember: b² - 4ac

a)

256 - 2 reals - Rational

b)

√(-256 - 2 imaginary solutions

c)

√(137) - 2 reals - Irrational

d)

123 - 2 reals - Rational

61.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

62.

Does this graph have a maximum or minimum?

a)

Minimum

b)

Maximum

63.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

line of dashes

64.

What is the axis of symmetry for this graph?

a)

y=2

b)

x=2

c)

x=0

d)

y=0

65.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

66.

The line that goes through the vertex of a parabola is called the...

a)

Vertex

b)

Axis of Symmetry

c)

x-intercept

d)

y-intercept

67.

The vertex of this quadratic is...

a)

(1,16)

b)

(-3,0)

c)

(5,0)

d)

(0,15)

68.

Which letter determines if a parabola opens up or down?

a)

a

b)

h

c)

k

69.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

70.

What is the vertex?

a)

(4,-4)

b)

(2,0)

c)

(0,2)

d)

(6,0)

71.

The equation for the axis of symmetry line is x = -b/(2a)

a)

true

b)

false

72.

What's the axis of symmetry of y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

73.

Does the equation open or or down?
Y = -3x² +7x - 2

a)

up

b)

down

74.

Does the equation have a max or min?
y = 2x² + 7x + 5

a)

max

b)

min

75.

What is the axis of symmetry?

a)

the slope of the graph

b)

the dividing line for a parabola

c)

a way to spin my pencil

d)

the x-axis

76.

What's the axis of symmetry of y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

77.

The equation for the axis of symmetry line is

x=\frac{-b}{2a}

a)

true

b)

false

78.

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

79.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

80.

What should you do first in solving this equation?

x² + 6x - 13 = 3

a)

Factor

b)

Write down: a = 1, b = 6, c = -13

c)

Subtract 3 from both sides.

d)

Add 3 to both sides.

81.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

82.

2x²-x -3=0

a)

x=-3/2 x=1

b)

x= 3/2 x= -1

c)

x= -3/2 x= -1

d)

x= 3/2 x= 1

83.

$2r^2+3r-1=0$

Solve using the quadratic equation.

4 lines

84.

$2m^2=-2m+12$
Solve using the quadratic formula.

a)

$x=2,-3$

b)

$x=3,-2$

c)

$x=1\pm\sqrt{13}$

d)

No Solution

85.

Solve using the quadratic formula...

9x² = 4 + 7x

a)

b)

c)

d)

No solution

86.

Solve using the quadratic formula:

4x²+ 4x + 1 = 0

a)

x = -½

b)

x = -2

c)

x = 0

d)

x = ½

87.

What is the "c" value in the equation..

4x^2=18

a)

4

b)

18

c)

0

d)

-18

88.

Identify the transformation of the equation.
y = x² + 5

a)

Shifted right

b)

Shifted down

c)

Shifted up

d)

Shifted left

89.

Identify the transformation of the equation.
y = (x - 8)²

a)

Shifted right

b)

Shifted down

c)

Shifted up

d)

Shifted left

90.

Identify the transformation of the equation.
y = -x²

a)

Reflected over y-axis

b)

Reflected over x-axis

c)

Narrowed

d)

Widened

91.

Identify the transformation of the equation.
y = 4x²

a)

Shifted up

b)

Reflected over x-axis

c)

Narrowed

d)

Widened

92.

Which equation shifts the parent function left?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² + 4

d)

y = x² - 4

93.

Identify the transformation of the equation.
y = 0.9x²

a)

Shifted right

b)

Reflected over x-axis

c)

Narrowed

d)

Widened

94.

Which equation shifts the parent function right?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² + 4

d)

y = x² - 4

95.

Identify the transformation of the equation.
y = (x + 4)²

a)

Shifted right

b)

Shifted left

c)

Shifted up

d)

Shifted down

96.

Which equation compresses the parent function?

a)

y = 4x²

b)

y = 0.4x²

c)

y = x² + 4

d)

y = -x²

97.

Identify the transformation of the equation.
y = 3x²

a)

Shifted right

b)

Reflected over x-axis

c)

Narrowed

d)

Shifted left

98.

Which equation shifts the parent function down?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² + 4

d)

y = x² - 4

99.

Identify the transformation of the equation.
y = 1.3x²

a)

Shifted right

b)

Reflected over x-axis

c)

Narrowed

d)

Widened

100.

Identify the transformation of the equation.
y = x² - 9

a)

Shifted right

b)

Shifted left

c)

Shifted up

d)

Shifted down

101.

Identify the transformation of the equation.
y = (x + 1)²

a)

Shifted right

b)

Shifted left

c)

Shifted up

d)

Shifted down

102.

Which equation stretches the parent function?

a)

y = 4x²

b)

y = 0.4x²

c)

y = x² + 4

d)

y = -x²

103.

Identify the transformation of the equation.
y = 0.2x²

a)

Shifted right

b)

Shifted left

c)

Compressed

d)

Stretched

104.

Which equation reflects the parent function over the x-axis?

a)

y = 4x²

b)

y = 0.4x²

c)

y = x² - 4

d)

y = -x²

105.

Identify the transformation of the equation.
y = x² - 7

a)

Shifted right

b)

Shifted left

c)

shifted down

d)

Shifted up

106.

Identify the transformation of the equation.
y = 5x²

a)

Shifted right

b)

Shifted left

c)

Stretched

d)

Compressed

107.

Which equation shifts the parent function up?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² + 4

d)

y = x² - 4

108.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

109.

Factor: x² + 2x – 3

a)

(x - 2)(x + 1)

b)

(x + 1)(x - 3)

c)

(x + 2)(x - 1)

d)

(x - 1)(x + 3)

110.

Factor:

5x³- 7x²

a)

x²(5x - 7)

b)

x(5x²- 7x)

c)

x³(5 - 7x)

d)

Prime

111.

Factor: 25x²- 9

a)

(5x + 3)(5x - 3)

b)

(x + 5)(x - 3)

c)

(x - 3)(x + 5)

d)

(5x + 3)(3x + 5)

112.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

113.

Factor:
x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

114.

What are the factors of x²+3x-40

a)

(x+10)(x-4)

b)

(x+8)(x-5)

c)

(x+20)(x-2)

d)

(x+1)(x-3)

115.

Factor:
24c⁵ - 12c³

a)

6(4c⁵ - 2c³)

b)

12c³(2c²)

c)

12c³(2c² - 1)

d)

12c³(2c² - 0)

116.

Factor d² - 10d + 25

a)

(d + 5) (d - 5)

b)

(d - 15) (d + 10)

c)

(d + 5) (d - 20)

d)

(d - 5) (d - 5)

117.

Factor: 6x² + 9x

a)

(6x + 1)(x + 3)

b)

(3x + 1)(2x + 3)

c)

3x(2x + 3)

d)

6x(x + 3)

118.

Factor:
6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

119.

Factor:
12x + 9

a)

3(4x + 3)

b)

x(12+9)

c)

3(4x - 3)

d)

not factorable

120.

Find GCF 15n³+25n²

a)

5

b)

15n

c)

5n²

d)

5n

121.

Factor:
5x³-7x²

a)

x²(5x-7)

b)

x(5x²-7x)

c)

x³(5-7x)

d)

Prime

122.

Factor: 49x² - 100

a)

(49x + 100)(x - 1)

b)

(7x - 10)(7x + 10)

c)

(49x - 10)(x + 10)

d)

(7x -10)(7x - 10)

123.

x²+4x-32=0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

124.

a)

A

b)

B

c)

C

d)

D

125.

What are the factors of x²-8x-48

a)

(x-12)(x+4)

b)

(x+12)(x-4)

c)

(x+12)(x+4)

d)

(x-12)(x-4)

126.

Find the factors of x²-81

a)

(x-9)(x+9)

b)

(x+9)(x+9)

c)

(x-9)(x-9)

d)

Can't be factored

127.

Factor:

5x² + 20

a)

5(x + 4)

b)

5x(x + 4)

c)

5(x² + 4)

d)

5x²(x + 4)

128.

x² - 9

a)

(x + 3)²

b)

(x + 3) (x - 3)

c)

(x - 3)²

d)

x + 3(x - 3)

129.

x² - 16

a)

(x + 4) (x - 4)

b)

(x + 8) (x - 2)

c)

(x + 4)²

d)

x + 4(x - 4)

130.

4x² - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

131.

25x² - 36y²

a)

5x + 6y(5x - 6y)

b)

(5x + 6y) (5x - 6y)

c)

(5x + 6y)²

d)

(5x - 6y)²

132.

4x²y² - 1

a)

(2 + xy) (2 - xy)

b)

(2x + y) (2x - y)

c)

(2xy + 1) (2xy - 1)

d)

(2y + x) (2y - x)

133.

64x² - 81y²

a)

(8x + 7y) (8x - 7y)

b)

(8x + 9y) (8x - 9y)

c)

(6x + 7y) (6x - 7y)

d)

(6x + 9y) (6x - 9y)

134.

4x² - 16

a)

4(2x + 4) (x - 2)

b)

4(4x + 2) (x - 2)

c)

(2x + 4) (2x - 4)

d)

4(x + 2) (x - 2)

135.

49x² - 144y²

a)

(7x + 16y) (7x - 16y)

b)

(7x + 12y)²

c)

(12x + 7y) (12x - 7y)

d)

(7x + 12y) (7x - 12y)

136.

Factor 4y² – 9.

a)

(2y + 3)(2y – 3)

b)

prime

c)

(2y + 3)(2y + 3)

d)

(2y – 3)(2y – 3)

137.

Factor completely.

x² - 144

a)

( x - 12 ) ²

b)

( x - 12 ) ( x - 12 )

c)

( x + 12 ) ( x + 12 )

d)

( x + 12 ) ( x - 12 )

138.

Factor completely.

y² - 196

a)

( y - 14 ) ( y - 14 )

b)

( y + 14 ) ( y - 14 )

c)

( y + 13 ) ( y - 13 )

d)

( y - 13 ) ²

139.

Factor completely.

121x² - 49

a)

( 11x - 7 ) ²

b)

( 11x - 7 ) ( 11x - 7 )

c)

( 11x + 7 ) ( 11x - 7 )

d)

( 12x + 7 ) ( 12x - 7 )

140.

Factor completely.

64x² - 49y²

a)

( 8x + 7 ) ( 8x - 7 )

b)

( 8x - 7y ) ( 8x - 7y )

c)

( 8x + 7y ) ( 8x - 7y )

d)

( 8x - 7y )²

141.

Factor completely.

225x² - 169y²

a)

( 15x - 13y )²

b)

( 15x + 13 ) ( 15x - 13 )

c)

( 25x + 13y ) ( 25x - 13y )

d)

( 15x + 13y ) ( 15x - 13y )

142.

Factor completely.

49x² + 16

a)

( 7x + 4 ) ( 7x - 4 )

b)

( 7x + 4 ) ( 7x + 4 )

c)

( 7x - 4 ) ²

d)

does not factor (SUM of squares)

143.

(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

144.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

145.

Simplify the expression.
x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

146.

Simplify the following expression:

(b³)⁸

a)

b¹¹

b)

8b³

c)

b²⁴

d)

24b

147.

Simplify the following expression:

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

148.

Simplify the following expression:

(3x⁴y⁵)²

a)

9x⁸y¹⁰

b)

6x⁸y¹⁰

c)

3x⁸y¹⁰

d)

x⁸y¹⁰

149.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

150.

Simplify the following expression:

(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

151.

According to exponent rules, when we raise a power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

152.

(2x⁷)³

a)

6x²¹

b)

8x²¹

c)

6x¹⁰

d)

8x¹⁰

153.

Which number is the BASE?

2³= 8

a)

2

b)

8

c)

3

d)

238

154.

Which number is the EXPONENT?

4^{2 =}16

a)

4

b)

16

c)

2

d)

162

155.

5², in this example, 5 is the ______ and 2 is the _______

a)

base, product

b)

exponent, base

c)

base, exponent

d)

product, base

156.

Write the product as a power :

(-2) ⋅ (-2) ⋅ (-2) ⋅ (-2) ⋅ (-2)

a)

-2⁵

b)

2^-5

c)

(-2)⁵

d)

(-2)^-5

157.

Which expression is in expanded form?

a)

5³

b)

5x5x5

c)

125

d)

53

158.

Which expression is equivalent to 3⁴?

a)

3+3+3+3

b)

4+4+4

c)

4x4x4

d)

3x3x3x3

159.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

160.

2²x 2³

a)

4⁶

b)

4⁵

c)

2⁶

d)

2⁵

161.

x^{20 .} x¹⁰

a)

x³⁰

b)

x²⁰⁰

c)

2x³⁰

d)

x¹⁰

162.

If the bases are the same, then you....

a)

Multiply the exponents

b)

Subtract the exponents

c)

Add the exponents

d)

Divide the exponents

163.

2 * 2² *2²

a)

2⁴

b)

8⁴

c)

36

d)

2⁵

164.

How do you correctly say 4³

a)

4 squared

b)

3 quadrupled

c)

4 cubed

d)

4 to the power of 2

165.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

166.

(5²)³

a)

5⁶

b)

5⁵

c)

5⁷

d)

5⁸

167.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

168.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

169.

Simplify

a)

x⁴/3

b)

3x¹⁰

c)

36x¹⁰

d)

3x⁴

170.

Evaluate the expression using the quotient of powers rule.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

a⁸b⁷

171.

True or False:

a)

True

b)

False

172.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

173.

Simplify the expression.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

174.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

175.

a)

3x^-1y^-5

b)

3x²y

c)

3xy⁵

d)

-3x³y⁷

176.

a)

x⁴y⁴

b)

x⁸y⁴

c)

x^-4y¹²

d)

x⁸y¹²

177.

Simplify the following:
(x²y)⁵

a)

x⁷y⁵

b)

x²y⁵

c)

x¹⁰y⁵

d)

x⁵y⁵

178.

Simplify the expression

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

179.

Simplify

\frac{x^7y^5}{xy^2}

a)

$x^6y^7$

b)

$x^8y^7$

c)

$x^7y^{10}$

d)

$x^6y^3$

180.

Simplify

\left(x^4\right)^6

a)

$x^{10}$

b)

$x^{-2}$

c)

$x^2$

d)

$x^{24}$

181.

Rewrite the following

∛x⁵

a)

x^3/5

b)

x^5/3

c)

x²

d)

x³⋅x⁵

182.

Write as a radical expression
y²⁄ ³

a)

2y³

b)

√y³

c)

∛y²

d)

3y²

183.

Simplify

a)

3 x² y² z √3yz

b)

3 x y z √xy²

c)

3xyz

d)

Can't Simplify

184.

a)

11√5

b)

11√10

c)

5√5

d)

12√10

185.

Re-write the expression in radical form.
x^2/3

a)

∛x²

b)

√x³

c)

(1/x)

d)

∛x

186.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

187.

14

a)

a

b)

b

c)

c

d)

d

188.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

189.

If the expression written as $\sqrt[5]{7}\cdot\sqrt[3]{7}$ is written as $7^n$ , what is the value of n?

a)

8

b)

15

c)

$\frac{3}{5}$

d)

$\frac{8}{15}$

190.

Simplify the expression.

$\sqrt[3]{x^2}\cdot\sqrt[3]{x^4}$

a)

$\sqrt[9]{x^6}$

b)

$x^6$

c)

$x^8$

d)

$\sqrt[6]{x^8}$

191.

Simplify the expression.

$\frac{\sqrt[3]{x}}{\sqrt[4]{x}}$

a)

$\sqrt[12]{x}$

b)

$\sqrt[]{x}$

c)

$-\sqrt[]{x}$

d)

$x^{12}$

192.

Write the expression in radical form.
x^7/2

a)

√x⁷

b)

7√x²

c)

7x²

d)

∛x⁷

193.

Write the expression in exponential form:
∜x⁵

a)

x^4/5

b)

x^5/4

c)

x⁵

d)

x^1/4

194.

Write with radical. Assume that all variables represent positive real numbers.

$\left(x^4y^4\right)^{\frac{1}{7}}$

a)

$\left(\sqrt[7]{xy}\right)^4$

b)

$x^{28}y^{28}$

c)

$\frac{1}{\left(\sqrt[7]{xy}\right)^4}$

d)

$\left(\sqrt[4]{xy}\right)^7$

195.

Write with radical. Assume that all variables represent positive real numbers.

$\left(5py^2\right)^{\frac{1}{3}}$

a)

$\sqrt[3]{5py}^{ }$

b)

$\sqrt[3]{5py^2}$

c)

$\sqrt[]{5py^2}$

d)

$\sqrt[5]{5py}^{ }$

196.

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

$\sqrt[4]{s^7}.\sqrt[3]{s^5}$

a)

$s^{\frac{41}{12}}$

b)

$\sqrt[7]{s^{40}}$

c)

$s^{6.325}$

d)

$\sqrt[]{s^{35}}$

Intermediate Algebra Review

Total questions: 196

Worksheet time: 49hrs 0mins

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