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5. Indices and Surds
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iGCSE (2021 Edition)

5.01 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

0607C1.9A

Meaning of exponents (powers, indices) in Z. Rules for exponents.

0607E1.9A

Meaning of exponents (powers, indices) in Z. Rules for exponents.

0607C2.4

Simple indices – multiplying and dividing.

0607E2.4

Indices.

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