Topics
1. The real numbers
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Australia
Year 9

1.03 Exponents

Lesson
Worksheet
Practice
Worksheet
Indices
1

Evaluate the following:

a
3^{1}
b
1^{3}
c
2^{6}
d
\left( - 2 \right)^{4}
e
\left( - 4 \right)^{3}
f
- 4^{3}
g
\left( - 3 \right)^{4}
h
- 3^{4}
i
\left( - 4 \right)^{2}
j
\left( - 16 \right)^{2}
k
- 15^{2}
l
- \left( - 8 \right)^{2}
2

Evaluate:

a
9^{2} + 6
b
9^{2} - 8^{2}
c
3^{2} + 7^{2}
d
15 - 3^{2}
e
5^{2} + 8^{2}
f
4^{2} - 2^{3}
g
7^{2} + 18
h
28 + 6^{2}
3

Evaluate the following:

a
5 \times 2^{3}
b
-7 \times 3^{4}
c
5^{2} \times 9^{2}
d
-3^{2} \times 4^{3}
4

Evaluate the following:

a
\left( - 9 \right) \times \left( - 6 \right)^{2}
b
4 - \left(5 - 2\right)^{2}
c
6 - \left(12 - 3^{2}\right)
d
9 - 2^{2} \times \left( - 7 \right)
e
\left(2 - 5\right)^{2} \times \left( - 21 + 14\right)
f
- \left( - 4 \right)^{3} - \left( - 10 \right)^{2} - 122
5

State whether the following expressions are positive, negative or zero:

a
- 3^{6}
b
-5^{7}
c
\left( -3 \right)^{ 5 }
d
\left( -5 \right)^{ 8 }
6

Evaluate the following:

a
3^{3} \div 3^{2}
b
4^{7} \div 3^{5}
c
\dfrac{6^4}{6^2}
d
\dfrac{-7^5}{7^4}
7

Evaluate the following:

a
7 \times \left(5^{6} \div 5^{4}\right)
b
\left(-4+7\right)^{2} \div \left( 9-12\right)
c
-64 \div \left(8 - 6\right)^{5}
d
\left(54 \div 3^3\right) \times \left( -4^2+25\right)
8

Convert the following into index form using positive indices:

a
27
b
121
c
–128
d
1000
Applications
9

Paulina forwards a social media post to 7 of her friends. Each of her 7 friends forwards it 7 other friends and each of these people also sends it to 7 other friends.

How many people are reached by the social media post, excluding those who forwarded the message?

10

The population of rabbits in a shelter is doubling every hour. If there are 15 rabbits initially, find the number of rabbits after:

a

3 hours

b

5 hours

c

8 hours

d

10 hours

11

A broker mentioned that he can triple Lawrence's money every year. Lawrence invest \$200 with the broker.

How much should Lawrence's investment after 3 years?

12

Sally is reading a 500-page book that she wants to finish in 5 days. She starts off by reading 15 pages on the first day, but quicky realises that she needs to read more to finish the book in time. She decides to double the number of pages she reads each day.

How many pages has she read on the:

a

2nd day?

b

4th day?

c

5th day?

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Outcomes

AC9M9A01

apply the exponent laws to numerical expressions with integer exponents and extend to variables

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