Free Printable Product Rule, Power Rule, Quotient Rule and Zero Exponent Rule

1.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

2.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

3.

Simplify the expression:
5²⋅5¹=

a)

5³

b)

5³⁺¹

c)

5²

4.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

5.

Simplify the following expression:

r⁶⋅ r²⋅ r³

a)

r⁶²³

b)

r¹¹

c)

11r

d)

r³⁶

6.

Simplify the following expression:

3x⁴ ⋅ 6x⁶

a)

18x¹⁰

b)

9x¹⁰

c)

18x²⁴

d)

9x²⁴

7.

Simplify the following expression:

2x³y⁵ ⋅ 5xy²

a)

10x⁴y⁷

b)

7x⁴y⁷

c)

10x³y¹⁰

d)

7x³y¹⁰

8.

Simplify the following expression:

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

9.

Simplify the following expression:

(-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

10.

Simplify the following expression:

(-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

11.

Simplify the following expression:

5a³b⁵⋅ 3a²b²

a)

8a⁵b³

b)

15a⁵b⁷

c)

8a⁵b⁷

d)

15a⁵b³

12.

Simplify the expression.
(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

13.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

14.

Simplify:

$x^4\left(x^{12}\right)$

a)

$x^3$

b)

$x^{48}$

c)

$x^{16}$

d)

$x^8$

15.

$10^3=$

a)

$10\times10\times10$

b)

$10\times3$

c)

$10+10+10$

d)

10,000

16.

$10\times10\times10\times10\times10=$

a)

$10\times5$

b)

$10^5$

17.

$m^2\cdot m^6\cdot m=$

a)

$m^8$

b)

$m^{12}$

c)

$m^4$

d)

$m^9$

18.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

19.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

20.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

21.

$3^2\ \cdot\ 3^4$

a)

$3^6$

b)

$9^6$

c)

$3^8$

d)

$9^8$

22.

$m\ \cdot\ m^4$

a)

$2m^4$

b)

$2m^5$

c)

$m^5$

d)

$m^4$

23.

$3g^6\ \cdot\ 2g^2$

a)

$6g^8$

b)

$6g^{12}$

c)

$3g^2$

d)

$2g^6$

24.

$4h^3\ \cdot\ 5h^4$

a)

$9h^{12}$

b)

$9h^7$

c)

$20h^7$

d)

$20h^{12}$

25.

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

a)

$y^{72}$

b)

$9y^{72}$

c)

$9y^8$

d)

$y^{17}$

26.

Simplify $\left(5^3\right)^{10}$

a)

$25^3$

b)

$5^{13}$

c)

$25^{30}$

d)

$5^{30}$

27.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

28.

Simplify the following expression:

(3x⁴y⁵)²

a)

9x⁸y¹⁰

b)

6x⁸y¹⁰

c)

3x⁸y¹⁰

d)

x⁸y¹⁰

29.

(2ab)³

a)

8a³b³

b)

2ab³

c)

6a³b³

d)

6ab

30.

Which of the following expressions is equivalent to (2x)³ ?

a)

(2x)(2x)(2x)

b)

2(x)(x)(x)

c)

2x + 2x + 2x

d)

2x⋅3

31.

(5³)⁷

a)

5²¹

b)

5¹⁰

c)

5⁴

d)

125²¹

32.

Simplify (-9)⁰

a)

-9

b)

-1

c)

1

d)

9

33.

$\left(3x\right)^3$

a)

$9x^3$

b)

$x^3$

c)

$3^3x^3$

d)

$6x^3$

34.

(5²)³

a)

5⁶

b)

5⁵

c)

5⁷

d)

5⁸

35.

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

a)

add

b)

subtract

c)

multiply

d)

divide

36.

Simplify the following expression:

(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

37.

What's the base?
y⁵

a)

5

b)

y

38.

a)

3

b)

0

c)

1

d)

1/3

39.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

40.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

41.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

42.

Simplify the expression.

a)

y¹⁵

b)

y⁵⁰

c)

y²

d)

y⁵

43.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

44.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

45.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

46.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

47.

True or False:

a)

True

b)

False

48.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

49.

Simplify the expression:
(5⁸) ÷ (5²)

a)

5⁶

b)

5¹⁰

c)

5⁴

d)

5¹⁶

50.

True or False?

a)

True

b)

False

51.

Quotient Rule states: keep the base the same and do this to the exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

52.

Simplify the expression.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

53.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

54.

4x4x4x4x4x4x4 as an exponent is ...

a)

4¹

b)

4⁵

c)

4⁷

55.

1⁹⁹is equivalent to ...

a)

99

b)

1

c)

0

d)

199

56.

100¹is the same as ...

a)

100

b)

1000

c)

1

d)

10

57.

9x9x9x9x9 written in exponential form is

a)

9⁵

b)

9³

c)

9¹⁰⁰

58.

$\left(2^8\right)^2$

a)

$2^{16}$

b)

$2^{10}$

c)

$2^6$

d)

$2^4$

59.

Which number is the EXPONENT?
4^{2 =}16

a)

4

b)

2

c)

16

60.

Simplify 4²· 4

a)

16²

b)

16³

c)

4²

d)

4³

61.

Simplify (b⁴)²

a)

b⁶

b)

b⁸

c)

2b⁴

d)

b¹⁶

62.

Simplify 487⁰

a)

0

b)

1

c)

487

d)

undefined

63.

x⁵

x⁹

a)

x⁴

b)

x^-4

c)

1

x⁴

d)

undefined

64.

x^{20 .} x¹⁰

a)

x³⁰

b)

x²⁰⁰

c)

2x³⁰

d)

x¹⁰

Product Rule, Power Rule, Quotient Rule and Zero Exponent Rule

Total questions: 64

Worksheet time: 3hrs 58mins

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