Free Printable Exponent and Radicals Test

1.

Which is equivalent to

7 x 7 x 7 x 7 x 7 x 7 ?

a)

7⁵

b)

7⁶

c)

6⁷

d)

7⁷

2.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

3.

Simplify
m⁵⋅m²

a)

m⁷

b)

m³

c)

m¹⁰

d)

m²

4.

Simplify

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

a⁸b⁷

5.

Simplify the following: (v⁴)⁹

a)

v³⁶

b)

v¹³

c)

v⁵

d)

v^-5

6.

Simplify the following:

(r²s³t)⁸

a)

r¹⁶s²⁴t⁸

b)

r¹⁰s¹¹t⁸

c)

r¹⁰s¹¹t⁹

d)

r¹⁶s²⁴t⁹

7.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

8.

Rewrite using a positive exponent.
g^-7

a)

¹/_g⁷

b)

g⁷

c)

¹/_g^-7

d)

-g⁷

9.

Simplify so that there are no negative exponents.

a)

y

b)

y⁵

c)

y¹⁵

d)

2y⁵

10.

Simplify each expression so that it contains only positive exponents.

a)

b)

c)

d)

11.

Change this expression to a Radical

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

a)

1∕ 3y

b)

y³

c)

√y

d)

∛y

12.

Which expression with a fractional exponent best represents √7 ?

a)

7^½

b)

7¼

c)

7⅓

d)

2⁷

13.

Write in exponential form

∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

14.

Rewrite x^3/4 in radical form

a)

³√(x)⁴

b)

⁴√(x)³

c)

^x√(3)⁴

d)

1/(³√(x)⁴)

15.

What is the prime factorization of 8?

a)

4*2

b)

2*2*2

c)

2+2+2

16.

Is 5 prime or composite?

a)

Prime

b)

Composite

17.

A prime number

a)

has one factor

b)

has more than 2 factors

c)

has 100 factors

d)

has exactly 2 factors: 1 and the number

18.

Use a factor tree to find the prime factorization of 60

a)

5x3x2x2

b)

7x6x5

c)

5x3x3x2

d)

7x5x4

19.

All of these are prime except

a)

3

b)

9

c)

2

d)

13

20.

Simplify:

(√6)(√2)

a)

√10

b)

2√3

c)

√8

d)

4√3

21.

Simplify: $\sqrt{20}$

a)

$2\sqrt{3}$

b)

$4\sqrt{5}$

c)

$2\sqrt{5}$

d)

$5\sqrt{5}$

22.

Simplify $\sqrt{80}$

a)

$5\sqrt{4}$

b)

$4\sqrt{5}$

c)

$2\sqrt{5}$

d)

$5\sqrt{2}$

23.

Combine Like Terms:

a)

11√5

b)

11√10

c)

5√5

d)

12√10

24.

Combine Like Terms:

a)

17√2

b)

9√1

c)

9

d)

9√2

25.

Simplify:

a)

1/25

b)

2/50

c)

1/5

d)

1/√25

26.

Simplify

a)

40

b)

√14

c)

-10√10

d)

2√10

27.

Simplify the expression:

a)

√2 - 3√3

b)

2√-59

c)

-2√2 - 3√3

d)

-3.782

28.

Simplify:

a)

√12

b)

(4√3)/3

c)

√3

d)

(2√3)/3

29.

Simplify:

a)

√5

b)

(√14)/2

c)

√7

d)

Cannot be simplified

30.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

31.

$-\sqrt{2}+\sqrt{8}-3\sqrt{20}$

a)

$3\sqrt{2}-6\sqrt{5}$

b)

$-5\sqrt{3}$

c)

$\sqrt{2}-6\sqrt{5}$

d)

$\sqrt{4}-6\sqrt{5}$

32.

Simplify.

a)

5x⁸y¹⁰√10x

b)

5x⁴y⁵√10x

c)

5x⁴y⁵√2x

d)

5√2x⁹y¹⁰

33.

$5\sqrt{3}+\sqrt{12}$

a)

$7\sqrt{3}$

b)

$9\sqrt{3}$

c)

$5\sqrt{15}$

d)

$6\sqrt{3}$

34.

2√5 - √5 + 4√5 + √3

a)

6√5 + √3

b)

5√5 + √3

c)

6√5

d)

6√3

35.

Solve for V

a)

v=-81

b)

v=81

c)

v=9

d)

v=3

36.

Solve for n.

a)

n=25

b)

n=-25

c)

n=5

d)

n=-5

37.

Simplify:

a)

a

b)

a²

c)

a³

d)

a⁴

38.

Solve for x.

a)

-13

b)

4

c)

19

d)

Extraneous root

39.

$\left(2x-8\right)^{\frac{2}{3}}=4$ Solve the equation for x.

a)

x = 8

b)

x = 0

c)

x = 7

d)

no solution

40.

Simplify the following:
$\left(x^3y\right)^2$

a)

$x^5y^2$

b)

$x^6y^2$

c)

$x^1y^{-1}$

d)

$2x^3y$

41.

Solve for x:

$27\ =\ ^3\sqrt{x^9}$

a)

x = 3

b)

x = 9

c)

x = 6

d)

x = -3

42.

Simplify the following: $\left(x^2y\right)^3\sqrt{y^4}$

a)

$x^5y^6$

b)

$x^5y^5$

c)

$x^6y^6$

d)

$x^6y^5$

43.

Solve for x

a)

x=27

b)

x=-3

c)

x=81

d)

x=3

44.

Solve for x:
$\left(x-2\right)^{\frac{1}{3}}-3=-5$

a)

x = -6

b)

x = 3

c)

x = 7/3

d)

x = -5

45.

Solve for k:

a)

No Solution

b)

k = 2

c)

k = 0.5

d)

k = 3.74

Exponent and Radicals Test

Total questions: 45

Worksheet time: 5hrs 35mins

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