 Middle Years

1.06 Powers of whole numbers

Worksheet
Index notation
1

State the base for the expression 9^{5}.

2

State the power for the expression 2^{7}.

3

Write the following powers of 9 in index form:

a

9 \times 9

b

9 \times 9 \times 9

c

9 \times 9 \times 9 \times 9

d

9 \times 9 \times 9 \times 9 \times 9

4

Write the following expressions using index notation:

a

5 \times 5 \times 5

b

4 \times 4 \times 4 \times 4 \times 4

c

(-9) \times (-9) \times (-9) \times (-9)

d

7 \times 7

e

12 \times 12 \times 9 \times 9 \times 9

f

(-13) \times (-13) \times (-13) \times (-13) \times 5 \times 5

g

11 \times 7 \times 11 \times 7 \times 7

h

3 \times (-4) \times 3 \times 3 \times (-4)

i

(-6) \times (-2) \times (-6) \times (-6) \times (-2)

j

12 \times 12 \times 12 \times 15 \times 15

k

2 \times 4 \times 2 \times 4

l

24 \times 24 \times 24 \times 12

5

Write the following statements using index notation:

a

Two squared

b

Three cubed

6

Evaluate the following:

a
2^{6}
b
(-3)^{3}
c
3^{3} \times 3^{2}
d
2^{3} \times 4^{2}
e
\dfrac{3^{5}}{3^{3}}
f
\dfrac{(-6)^{9}}{6^{7}}
g
2^{2} + 4^{3}
h
7^{2} + 3^{4}
i
12^{2} - 2^{2}
j
5^{3} - 3^{3}
k
3^{3}-2^{2} \times 4^{2}
l
(-6)^{2} - 3^{8} \div 3^{6}
Expanded notation
7

Write the following expressions in expanded form:

a

9^{2}

b

9^{3}

c

9^{4}

d

9^{5}

8

Complete the table below:

9

Write the following numbers in expanded form:

a
5^{2}
b

7^{5} \times 6^{4}

c

4^{6} \times 9^{2}

d

77^{5} \times 13^{2}

10

Consider the expression 5^{3}.

a

Write the expression in expanded form.

b