Free Printable Review Basic Index Laws (multiplication, division, zero)

1.

What is the correct law for multiplication? a^m x aⁿ=

a)

a^m+n

b)

a^m + aⁿ

c)

a^mxn

d)

a^mn

2.

What is the correct law for division? a^m ÷ aⁿ =

a)

a^m-n

b)

a^m - aⁿ

c)

a^m÷n

d)

a^m/n

3.

Simplify: b¹⁷ x b⁵

a)

b²²

b)

b⁸⁵

c)

(b²)²²

d)

b¹²

4.

Simplify: w²⁴ ÷ w⁸

a)

w¹⁶

b)

w³

c)

w³²

d)

w^24/8

5.

Simplify: f⁰

a)

1

b)

f

c)

f¹

d)

0

6.

Simplify: (3x²y³)⁰

a)

1

b)

0

c)

3

d)

3x²y³

7.

Simplify: 3x³ × 6x⁸

a)

18x¹¹

b)

18x²⁴

c)

9x¹¹

d)

9x²⁴

8.

Simplify: 42m¹² ÷ 7m⁶

a)

6m⁶

b)

6m²

c)

35m⁶

d)

35m²

9.

Simplify: 64x¹⁶y¹² ÷ 4x⁸y³

a)

16x⁸y⁹

b)

16x²y⁴

c)

60x⁸y⁹

d)

60x²y⁴

10.

What is the correct law for zero exponent? a⁰ =

a)

a¹

b)

1

c)

a

d)

0

11.

What is the missing factor?

a)

1

b)

2

c)

5

d)

8

12.

What are the missing factors?

a)

2 and 3

b)

3 and 6

c)

3 and 3

d)

1 and 9

13.

What is the missing factor?

a)

3

b)

5

c)

6

d)

7

14.

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 itself.

15.

What is 6⁷in expanded form?

a)

6 x 6 x 6 x 6 x 6 x 6 x 6

b)

6 + 6 + 6 + 6 + 6 + 6

c)

6 x 7

16.

Simplify 2×b×b×b×3

a)

2b³

b)

6b

c)

b⁶

d)

6b³

17.

p⁴

What is the base of the number given?

a)

1

b)

p

c)

4

d)

p⁴

18.

m⁸

What is the index of the number given?

a)

1

b)

8

c)

m

d)

m⁸

19.

Simplify the following: a⁰ + a⁰

a)

a⁰

b)

2a⁰

c)

1

d)

2

20.

Simplify: a¹÷a¹

a)

0

b)

1

c)

a²

21.

Write in index notation. 7 x 7 x 7 x 7 x 7 x 10

a)

7⁵+ 10

b)

7⁵x 10

c)

7⁵x 10¹

22.

Which is the base and which is the power? 5²

a)

5 is base and 2 is power

b)

5 is base and power

c)

2 is base and 5 is power

d)

2 is base and power

23.

Complete in index notation. (9²)⁴

a)

9⁸

b)

9⁶

c)

9²

d)

none of the above

24.

Index form:
$a^n$ = a to the power of n

Which is represent to base?

a)

a

b)

n

25.

$5\times5\times5\times5\times5\times5\times5$

Write the repeated multiplication in index form, $a^n$ .

a)

$5^5$

b)

$5^7$

c)

$7^5$

d)

$78125$

26.

What is $2^3$ in expended form?

a)

$2\times2\times2$

b)

$3\times3$

c)

$2\times3$

d)

$3\times2$

27.

$m^3\times m=\ ??$

a)

$m$

b)

$m^4$

c)

$m^3$

d)

$m^2$

28.

$2^{-5}\times2^8=\ ??$

a)

$2$

b)

$2^{13}$

c)

$2^8$

d)

$2^3$

29.

Express $7\times7\times7\times7$ in index notation.

a)

$7\times4$

b)

$4\left(7\right)$

c)

$4^7$

d)

$7^4$

30.

How do you use indicies/exponents to represent numbers?

a)

repeated multiplication

b)

repeated addition

c)

repeated subtraction

d)

repeated division

31.

The exponent tells me...

a)

the answer

b)

the trick

c)

the number of times to multiply the base (factor)

d)

The number of days in a week

32.

24⁷ , in this example 7 is the _____________

a)

base

b)

exponent

33.

Simplify $\sqrt{49}$ .

a)

$5$

b)

$6$

c)

$7$

d)

$8$

34.

What is the value of $3^4$ ?

a)

$12$

b)

$27$

c)

$64$

d)

$81$

35.

Which of the following is the expanded form of $10^2$ ?

a)

$10 \times 10$

b)

$10 + 10$

c)

$2 \times 10$

d)

$10^2$

36.

Simplify $\sqrt{100}$ .

a)

$5$

b)

$10$

c)

$15$

d)

$20$

37.

Express $x^2$ in expanded form.

a)

$x\times x$

b)

$x+x$

c)

$2\times2$

d)

$2x$

38.

Simplify $\sqrt[3]{8}$

a)

$2$

b)

2.8

c)

3

d)

8

39.

Which statement below is a true statement?

a)

In 7⁵, the exponent is 7

b)

7⁰= 1

c)

In 7⁵, the base number is 5

d)

7⁵ = 7x5

40.

100 is what?

a)

10²

b)

10³

c)

10¹

d)

10⁰

41.

True or False?
10³= 30

a)

true

b)

false

42.

What is the exponent also known as?

a)

The Base

b)

The Power

c)

The Index

d)

The Derivative

43.

Which is GREATER?
2⁷ or 7²

a)

2⁷

b)

7²

c)

Neither, they are equal

44.

A scientist reports that a bacteria culture contains 3⁴ bacteria.
How many bacteria is that?

a)

12

b)

81

c)

7

d)

95

Review Basic Index Laws (multiplication, division, zero)

Total questions: 44

Worksheet time: 50mins

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