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8. Indices
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iGCSE (2021 Edition)

8.01 Multiplying and dividing with indices

Lesson
Worksheet
Practice
Worksheet
Multiplying terms with indices
1

Write the following expressions in simplest index form.

a
2^{2} \times 2^{2}
b

3^{4} \times 3^{10}

c
5^{4} \times 5^{3}
d
6^{6} \times 6^{7}
e

11^{4} \times 3^{4}

f

17^{44} \times 17^{48}

g

30^{72} \times 52^{72}

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

\left(3^{7}\right)^{5}

j

\left(83^{19}\right)^{40}

k
2^{2} \times 2^{3} \times 2^{4}
l
2^{6} \times 2^{8} \times 2^{7} \times 2^{5}
m
- 9 \times 2^{2} \times 2^{6}
n
9 \times \left( - 10 \right)^{4} \times 10^{8}
o
\dfrac{5}{3} \times 4^{6} \times 4^{2}
p
\dfrac{2}{3} \times 7^{8} \times 7^{9}
2

Find the product of the following expressions.

a

3^{4} \times 3^{3}

b

9^{2} \times 9^{5}

c

2^{4} \times 7^{4}

d

5^{5} \times 3^{3}

e

\left(6^{2}\right)^{3}

f

\left(3^{5}\right)^{2}

g
6 \times 5^{2} \times 5^{3}
h
\dfrac{3}{4} \times 4^{4} \times 7^{3}
3

Find the value of the blank that will make the following equations true.

a

3^{5} \times 3^{⬚} = 3^{7}

b

5^{8} \times 5^{⬚} = 5^{12}

c

9^{⬚} \times 9^{6} = 9^{9}

d

31^{⬚} \times 31^{37} = 31^{56}

e

3^{11} \times \left(⬚\right)^{11} = 21^{11}

f

\left(⬚\right)^{30} \times 90^{30} = 3780^{30}

g

\left(11^{11}\right)^{⬚} = 11^{33}

h

\left(37^{⬚}\right)^{14} = 37^{700}

Dividing terms with indices
4

Write the following expressions in simplest index form.

a
3^{8} \div 3^{6}
b

5^{10} \div 5^{5}

c
6^{13} \div 6^{6}
d
10^{8} \div 10^{6}
e
15^{33} \div 15^{27}
f

21^{8} \div 3^{8}

g

37^{30} \div 37^{18}

h

650^{69} \div 50^{69}

i
\dfrac{10^{10}}{10^{3}}
j
\dfrac{18^{32}}{18^{23}}
k
\dfrac{\left( - 7 \right)^{11}}{\left( - 7 \right)^{5}}
l
\dfrac{\left( - 10 \right)^{12}}{\left( - 10 \right)^{4}}
m
\dfrac{- 7^{8}}{7^{2}}
n
\dfrac{16^{32}}{- 16^{24}}
o
\dfrac{5 \times 4^{8}}{4^{2}}
p
\dfrac{4^{10}}{5 \times 4^{3}}
5

Find the quotient of the following expressions.

a

3^{9} \div 3^{4}

b

4^{4} \div 2^{4}

c
4^{7} \div 4^{4}
d
4^{8} \div 4^{5}
e
\dfrac{2^{12}}{2^{8}}
f
\dfrac{3^{6}}{3^{3}}
g
\dfrac{5 \times 4^{5}}{4^{3}}
h
\dfrac{6 \times 5^{8}}{5^{6}}
6

Find the value of the blank that will make the following equations true.

a

5^{⬚} \div 5^{5} = 5^{7}

b

6^{9} \div 6^{⬚} = 6^{7}

c

11^{10} \div 11^{⬚} = 11^{4}

d

31^{⬚} \div 31^{21} = 31^{13}

e

14^{9} \div \left(⬚\right)^{9} = 7^{9}

f

\left(⬚\right)^{66} \div 30^{66} = 19^{66}

The zero index
7

Evaluate the following:

a

8^{0}

b

21^{0}

c
741^{0}
d
\left( - 983 \right)^{0}
e
\left(\dfrac{- 5}{8}\right)^{0}
f
\left(\dfrac{7}{9}\right)^{0}
g
\left( 2 \times 13\right)^{0}
h
4 \left( 2 \times 13\right)^{0}
i
65^{0} + 81^{0}
j
89^{0} - \left( - 95 \right)^{0}
k
72^{0} + 2^{3}
l
7^{0} + \left( 8 \times 7\right)^{0}
8

Find the value of the blank that will make the following equations true.

a
3^{⬚} = 1
b

6^{10} \div 6^{10} = 6^{⬚}

c

\dfrac{8^{⬚}}{8^{9}} = 8^{0}

d

\dfrac{9^{8}}{9^{⬚}} = 9^{0}

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Outcomes

0580C1.7A

Understand the meaning of indices (fractional, negative and zero) and use the rules of indices.

0580E1.7A

Understand the meaning of indices (fractional, negative and zero) and use the rules of indices.

0580C2.4

Use and interpret positive, negative and zero indices. Use the rules of indices.

0580E2.4A

Use and interpret positive, negative and zero indices. Use the rules of indices.

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