Free Printable Laws of positive indices

1.

It is a small number that tells us how many times a term has been multiplied by itself.

a)

Index

b)

Expanded Form

c)

Index Notation

d)

Base

2.

we can read this $4^3$

a)

4 to the superpower of 3

b)

4 by 3

c)

4 third

d)

'4 to the power of 3'

3.

What is the index of the following: $4^6$

(a)

4.

What is the base of the following: $8^6$

(a)

5.

Simplify the following expression: $8^2\times g^5\times8^6=$

a)

$8^{13}$

b)

$8g^{13}$

c)

$8^8\times g^5$

d)

Cannot be simplified

6.

Which is the base and which is the exponent? 5²

a)

5 is base and 2 is exponent

b)

5 is base and exponent

c)

2 is base and 5 is exponent

d)

2 is base and exponent

7.

$3a^3\ \times\ 5a^{5\ }=\ ?$

a)

$15a^8$

b)

$8a^8$

c)

$8a^{15}$

d)

$15a^{15}$

8.

$\left(2x^3\right)^3=?$

a)

$8x^9$

b)

$8x^6$

c)

$2x^9$

d)

$2x^6$

9.

Simplify the following expression:

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

10.

Simplify: 3⁵ x 3⁷

a)

3¹²

b)

9¹²

c)

3³⁵

d)

9³⁵

11.

$3^3\times5^3=$

a)

$15^6$

b)

$15^3$

c)

$9\times15$

d)

$\left(3\times5\right)^9$

12.

Evaluate

a)

5⁴

b)

5¹⁰

c)

25¹⁰

d)

none of the above

13.

$\left(x^3\right)^4$ can be simplified into

a)

$x^{12}$

b)

$x^7$

c)

$x^{81}$

d)

$x^{-1}$

14.

Simplify:

$4a^3\times7a^2$

15.

Simplify:

$21a^9\div7a^2$

16.

Simplify:

$-3a^{4b}\times6a^{7b}$

17.

Write a simpliﬁed expression for the area of the rectangle in the picture.

(Leave the unit out of your answer)

18.

Without using a calculator, simplify the expression below to ﬁnd the missing power.

19.

Without using a calculator, simplify the expression below to ﬁnd the missing power.

20.

Without using a calculator, simplify the expression below to ﬁnd the missing power.

Laws of positive indices

Total questions: 20

Worksheet time: 27mins

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