Free Printable Laws of Exponents

1.

$What\ is\ the\ equivalent\ \exp ression?\ x\cdot x\cdot x\cdot x\cdot x$

a)

$x^5$

b)

$5x$

c)

5+x

d)

5

2.

True or False

In the expression $a^6$ , a is the base.

4 lines

3.

Simplify the expression $s^5\cdot s^4\cdot s^3$ .

a)

$s^{23}$

b)

$s^{19}$

c)

$s^{12}$

d)

$s^{20}$

4.

Simplify the expression $c^3\cdot c^4$

a)

$c^{12}$

b)

$c^7$

c)

12c

d)

c

5.

Simplify the expression $s^5\cdot s^4\cdot s^3$ .

a)

$s^{23}$

b)

$s^{19}$

c)

$s^{12}$

d)

$s^{20}$

6.

a)

1¹⁰

b)

1²⁶

c)

z¹⁰

d)

z²⁶

7.

a)

y¹⁴

b)

y¹⁰

c)

1¹⁴

d)

1¹⁰

8.

a)

4³

b)

4¹⁵

c)

1³

d)

1¹⁵

9.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

10.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.

Example:

$\frac{h^8}{h^3}$

a)

add

b)

subtract

c)

multiply

d)

divide

11.

a)

1¹⁶

b)

1⁶

c)

13¹⁶

d)

13⁶

12.

Use the quotient rule to simplify the monomial.

a)

-9b²

b)

9b²

c)

-9a

d)

9ab

13.

Use the quotient rule to simplify the monomial.

a)

5x²y

b)

-5x^2z

c)

-5x²yz

d)

5xy²z

14.

2²x 2³

a)

4⁶

b)

4⁵

c)

2⁶

d)

2⁵

15.

4²* 4²

a)

16⁴

b)

4²

c)

4⁴

d)

8²

16.

2 * 2² *2²

a)

2⁴

b)

8⁴

c)

36

d)

2⁵

17.

What is the base in 2⁸ ?

a)

8

b)

2

18.

10⁵x 10⁷

a)

10²

b)

10³

c)

10¹²

d)

10¹³

19.

t⁹ x t⁸

a)

t¹

b)

t⁷²

c)

t¹⁷

d)

t

20.

y¹² x y¹⁰

a)

y²

b)

y²²

c)

y²⁰

d)

y¹²⁰

21.

2n⁴ * 6n⁴

a)

8n⁴

b)

12n⁸

c)

8n¹⁶

d)

none of the above

22.

(x³)(x²)

a)

x^-5

b)

x^-6

c)

x⁶

d)

x⁵

23.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

24.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

25.

Evaluate the expression using the quotient rule.

a)

3⁴

b)

1/3⁴

c)

3^-12

d)

3³²

26.

( x ³ ) ⁵ is an example of the "power of a power" rule. This means the exponents 5 and 3 are _______ together.

a)

added

b)

subtracted

c)

multiplied

d)

divided

27.

Solve. ( 5 ² ) ⁴

a)

5 ⁶

b)

5 ⁸

c)

5 ²

d)

5 ⁰

28.

Solve. ( 3 ² m ² n ² ) ⁴

a)

12m ⁶ n ⁶

b)

3 ⁶ m ⁶ n ⁶

c)

3 ⁸ m ⁸ n ⁸

d)

13 m ² n ²

29.

What is ( 2 ⁴ ) ⁵ as a single power ?

a)

2 ⁹

b)

2 ¹

c)

2 ⁶

d)

2 ²⁰

30.

Solve. ( - 3 c ² d ⁴ e ) ³

a)

27c ⁵ d ⁷ e ³

b)

- 27 c ⁶ d ¹² e ³

c)

- 9cde

d)

- 9c⁵ d ⁷ e ⁴

31.

(8⁵)³

a)

8⁸

b)

8¹⁵

c)

8²

d)

1/8²

32.

Simplify $\left(y^8\right)^9$

a)

$y^{72}$

b)

$9y^{72}$

c)

$9y^8$

d)

$y^{17}$

33.

Simplify the following expression:

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

34.

Simplify the following expression:

(3x⁴y⁵)²

a)

9x⁸y¹⁰

b)

6x⁸y¹⁰

c)

3x⁸y¹⁰

d)

x⁸y¹⁰

35.

$\left(7e^3\right)^0$

a)

1

b)

7

c)

$21x^3$

d)

$x^{10}$

36.

$\left(7e^3\right)^0$

a)

1

b)

7

c)

$21x^3$

d)

$x^{10}$

37.

3⁻⁴

a)

1 ⁄ 81

b)

-81

c)

81

d)

1 ⁄ 12

38.

7^-2

a)

49

b)

10/49

c)

-49

d)

1/49

39.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

40.

Solve 3^-3

a)

-27

b)

-9

c)

$-\frac{1}{9}$

d)

$\frac{1}{27}$

41.

Rewrite using a positive exponent.
w^-13

a)

-w¹³

b)

$\frac{1}{w^{13}}$

c)

$\frac{1}{w^{-13}}$

d)

w¹³

42.

Rewrite using a positive exponent.
2w^-13

a)

-w¹³

b)

$\frac{2}{w^{13}}$

c)

$\frac{2}{w^{-13}}$

d)

2w¹³

43.

Write with positive exponents:

a)

a^-2

b)

a²

c)

$\frac{1}{a^1}$

44.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

45.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

Laws of Exponents

Total questions: 45

Worksheet time: 2hrs 24mins

Similar Resources on Wayground