Free Printable 6 ABCD Index Laws Formative test

1.

Simplify: (b⁴ x c²) ÷ b³

a)

bc⁸

b)

cb⁸

c)

bc²

d)

cb²

2.

Simplify: $\frac{a^5b^{10}}{a^3b^3}$

a)

$a^8b^{13}$

b)

$a^2b^7$

c)

$a^{15}b^{30}$

3.

Simplify:
$\left(3ab^2\right)\left(-2b^{-3}\right)$

a)

$-\frac{6a}{b}$

b)

$-\frac{6a^2}{b}$

c)

$ab$

d)

$\frac{3a}{2b}$

4.

What is the value of (-2)³?

a)

-8

b)

-6

c)

6

d)

8

5.

(10³)⁶

a)

10¹⁸

b)

30⁶

c)

10⁹

d)

30³

6.

c³ ÷ c⁷

a)

c⁴

b)

c^-4

c)

c¹³

d)

c^-2

7.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

8.

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

9.

(4a)²=

a)

4a²

b)

16a²

c)

8a²

d)

8a

10.

x^-3

a)

1/x³

b)

1/x^-3

c)

3x

d)

1/3x

11.

Simplify the following: (3ab⁴)³

a)

9a³b¹²

b)

9a³b⁷

c)

27a³b¹²

d)

27a³b⁷

e)

3³a³b¹²

12.

a x a x a x a=

a)

4a

b)

a⁴

c)

a⁶

d)

a

13.

Solve 5³

a)

8

b)

15

c)

75

d)

125

14.

7⁰

a)

7

b)

1

c)

0

d)

70

15.

What is 4⁵in expanded form?

a)

4 x 5

b)

4 x 4 x 4 x 4 x 4

c)

5 x 5 x 5 x 5 x 5

d)

4+4+4+4+4

16.

What is 3^₂in expanded form?

a)

3 x 2

b)

3 + 2

c)

3 x 3

17.

a^m x aⁿ = ____

a)

a^m+n

b)

a^{m x n}

c)

a^2mn

18.

a³ x a⁵

a)

a¹⁵

b)

a²

c)

a⁸

d)

a^-2

19.

b⁹x b⁷

a)

b⁶³

b)

b¹⁶

c)

b¹⁵

d)

b²

20.

y⁸ ÷ y

a)

y⁸

b)

y³

c)

y⁹

d)

y⁷

21.

(y²)³

a)

y⁵

b)

y

c)

y²³

d)

y⁶

22.

What is 4⁶÷4²

a)

4³

b)

4⁴

23.

What is b³xb⁴÷b²?

a)

b⁷

b)

b⁵

c)

b⁶

d)

b^2.5

24.

What is 10⁶÷10²x10⁵

a)

10¹⁵

b)

10⁸

c)

10⁹

d)

10²⁰

25.

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

26.

What is the correct law for powers of powers? (a^m)ⁿ =

a)

a^m x aⁿ

b)

a^{m x n}

c)

a^m+n

d)

a^men

27.

Simplify: 42m¹² ÷ 7m⁶

a)

6m⁶

b)

6m²

c)

35m⁶

d)

35m²

28.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

13x²y²

c)

36xy³

d)

13x³y³

29.

Simplify: 64x¹⁶y¹² ÷ 4x⁸y³

a)

16x⁸y⁹

b)

16x²y⁴

c)

60x⁸y⁹

d)

60x²y⁴

30.

Simplify using only positive exponents: $5^{-8}$ equals (a)

Choose from the below words

5^8

\frac{1}{5^8}

\frac{1}{5^{-8}}

-5^8

31.

Simplify using only positive exponents: $y^{-3}$

a)

$3y$

b)

$-y^3$

c)

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

d)

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

32.

Simplify using only positive exponents: $xy^{-3}$

a)

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

b)

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

c)

$\frac{x}{y^{-3}}$

d)

$xy^3$

33.

(3+r²)³

a)

3³+ r⁶

b)

3³r⁶

c)

3⁴ +r⁵

d)

3r⁵

34.

Simplify the following $\left(\frac{x^4}{y^5}\right)^3$

a)

$\left(\frac{x^{34}}{y^{35}}\right)$

b)

$\left(\frac{x^7}{y^8}\right)$

c)

$\left(\frac{x^{12}}{y^{15}}\right)$

35.

Simplify using only positive exponents: $xy^{-3}$

a)

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

b)

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

c)

$\frac{x}{y^{-3}}$

d)

$xy^3$

36.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

37.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

38.

(a³)³×a

a)

a⁹

b)

a⁷

c)

a¹⁰

d)

a¹²

39.

Express b² in expanded form

a)

b+b

b)

b+b+b

c)

b×b

d)

2×b

40.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

41.

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

a)

add

b)

subtract

c)

multiply

d)

divide

42.

$\frac{b^8}{b^{12}}=$

a)

$b^4$

b)

$b^{-4}$

c)

$\frac{1}{b^4}$

d)

$\frac{1}{b^{-4}}$

43.

$e^{-3}=$

a)

$\left(e^1\right)^3$

b)

$\left(-e\right)^3$

c)

$\frac{e^{-1}}{3}$

d)

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

44.

x^-3

a)

1/x³

b)

1/x^-3

c)

3x

d)

1/3x

45.

$r^9\div r^3=$

a)

$r^3$

b)

$r^6$

c)

$r^{12}$

d)

$1^3$

46.

$t^{12}\div t^4=$

a)

$t^8$

b)

$t^3$

c)

$t^{16}$

d)

$3$

47.

$12w^{12}\div3w^3=$

a)

$4w^4$

b)

$4w^9$

c)

$9w^9$

d)

$4w^{15}$

48.

$a^{-4}=$

a)

$a^4$

b)

$\frac{1}{a^4}$

c)

$\frac{a}{4}$

d)

$\frac{4}{a}$

49.

$e^{-3}f^2=$

a)

$\ \frac{f^2}{e^3}$

b)

$\frac{1}{e^3f^2}$

c)

$e^3f^2$

d)

$ef^{-1}$

50.

$20m^8n^6\div5m^2n^2=$

a)

$4m^4n^3$

b)

$4m^6n^4$

c)

$4mn^{10}$

d)

$4\left(mn\right)^{10}$

6 ABCD Index Laws Formative test

Total questions: 50

Worksheet time: 2hrs 44mins

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