Free Printable Law of indices

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.

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

a)

a^mxn

b)

a^m+n

c)

a^m x aⁿ

d)

a^men

4.

Simplify: 2⁸ ÷ 2²

a)

2⁶

b)

2⁴

c)

2¹⁰

d)

1

5.

Simplify: 3x³ × 6x⁸

a)

18x¹¹

b)

18x²⁴

c)

9x¹¹

d)

9x²⁴

6.

Simplify: f⁰

a)

1

b)

f

c)

f¹

d)

0

7.

Simplify: 42m¹² ÷ 7m⁶

a)

6m⁶

b)

6m²

c)

35m⁶

d)

35m²

8.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

36xy³

c)

13x²y²

d)

13x³y³

9.

Simplify: (y⁷)²

a)

y¹⁴

b)

y⁴⁹

c)

y⁵

d)

y⁹

10.

Simplify: (3h²)³

a)

27h⁶

b)

27h⁵

c)

9h⁶

d)

9h⁵

11.

Simplify: (3a²b)² × (2ab)³

a)

72a⁷b⁵

b)

6a⁷b⁵

c)

36a⁵b⁴

d)

18a⁴b²

12.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

13.

Simplify: (3x)² × (2x³y)² ÷ 6y³

a)

6x⁸y^-1

b)

6x⁸y

c)

3x⁷y

d)

3x⁷y^-1

14.

Simplify: 3x³ × 6x⁸

a)

18x¹¹

b)

18x²⁴

c)

9x¹¹

d)

9x²⁴

15.

$\frac{x^4}{x}=$

a)

$\left(x\div1\right)^4$

b)

$x^{\left(4\div1\right)}$

c)

$x^{\left(4-0\right)}$

d)

$x^{\left(4-1\right)}$

16.

$\left(2^4\right)^3=$

a)

$8^3$

b)

$2^7$

c)

$2^{12}$

d)

$8^{12}$

17.

$2^{-3}=$

a)

$-8$

b)

$-6$

c)

$\frac{1}{8}$

d)

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

18.

$7^2\times7^3=$

a)

$7^5$

b)

$7^6$

c)

$14\times21$

d)

$49^{2\times3}$

19.

$x^{\frac{1}{2}}=$

a)

$\frac{1}{2}x$

b)

$\sqrt{x}$

c)

$\frac{1}{x^2}$

d)

$-x^2$

20.

$\left(2n^3\right)^{-5}=$ (2014Q1)

a)

$\frac{1}{32n^2}$

b)

$\frac{1}{32n^{15}}$

c)

$\frac{1}{10n^{125}}$

d)

$\frac{1}{10n^{243}}$

21.

Simplify 6²x 6³as a single number in index form.

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

22.

Find a¹⁰ ÷ a²

a)

a⁸

b)

a⁵

c)

a¹²

d)

a¹⁰²

23.

m² X n² X m³ X n =

a)

m⁵ X n³

b)

m⁴ X n⁴

c)

m⁴ X n³

d)

m⁶X n²

24.

$15m^3k^3\div3m^2k^5$

a)

5mk^{-2}

b)

$5mk^8$

c)

$5m^5$

d)

$5m^5k^8$

25.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

26.

Simplify 4⁰

a)

1

b)

4

c)

0

27.

What is the missing index?(2⁶)^x = 2¹⁸

a)

12

b)

3

c)

10

d)

4

28.

Solve 16^{2x - 1}= 64

a)

1.5

b)

1.25

c)

4/5

d)

-1.25

Law of indices

Total questions: 28

Worksheet time: 2hrs 20mins

Similar Resources on Wayground