IGCSEMaths: CoreCIEExam QuestionsAlgebra & SequencesAlgebraic Roots & Indices

Syllabus Edition

First teaching 2023

First exams 2025

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Algebraic Roots & Indices (CIE IGCSE Maths: Core)

Exam Questions

33 mins22 questions
Easy
Medium
Hard
1
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6 to the power of 10 cross times 6 to the power of x equals 6 squared

Find the value of x.

x equals........................

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2
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Find the value of x when 5 to the power of x cross times 5 cubed equals 5 to the power of 12

x equals............................

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3a
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Simplify.

p squared cross times p to the power of 4

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3b
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m to the power of 15 divided by m to the power of 5

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3c
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open parentheses k cubed close parentheses to the power of 5

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4
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9 to the power of 12 divided by 9 to the power of w equals 9 to the power of 4

Find the value of w.

w space equals................................

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5
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Simplify open parentheses w to the power of 5 close parentheses to the power of 4

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6a
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Simplify.

t to the power of 21 divided by t to the power of 7

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6b
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open parentheses u to the power of 5 close parentheses to the power of 5

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7
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Simplify

open parentheses x to the power of 8 close parentheses cubed

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8
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Simplify.

open parentheses y to the power of 5 close parentheses cubed

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9
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Simplify open parentheses x to the power of 5 close parentheses squared.

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10a
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x cubed cross times x to the power of 6 equals x to the power of m

Find the value of m.

m = ................................................... 

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10b
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open parentheses x squared close parentheses to the power of n equals x to the power of 12

Find the value of n.

n = ................................................... 

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1
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i)
2 to the power of 8 cross times 2 to the power of m equals 2 to the power of 6 

Work out the value of m.

m = ................................................. [1]

ii)
5 to the power of n divided by 5 to the power of 4 equals 5 to the power of 6

Work out the value of n.
n = ................................................. [1]

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2
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Simplify.

5 cross times x to the power of 0

[1]

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3
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Simplify 2 x cubed cross times 3 x squared

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4
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Simplify.

5 m squared cross times 2 m cubed

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5
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(i)
Find the value of k when x to the power of 10 divided by x to the power of k equals x cubed.

k space equals....................... [1]

(ii)
Find the value of n when y to the power of 10 cross times y to the power of n equals 1.

n space equals......................... [1]

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1
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Simplify.

4 p to the power of 5 q cubed space cross times p squared q to the power of negative 4 end exponent

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2
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Simplify 8 t to the power of 8 space divided by 4 t to the power of 4.

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3
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Simplify  x cubed y to the power of 4 cross times x to the power of 5 y cubed

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4
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Simplify

w to the power of 7 space divided by space w to the power of negative 2 end exponent

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5
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4 to the power of w space equals space 1 over 16

Find the value of w.

w space equals ...............................

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