Syllabus Edition

First teaching 2021

Last exams 2024

|

Algebraic Roots & Indices (CIE IGCSE Maths: Extended)

Exam Questions

2 hours44 questions
1
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1 mark

Simplify a squared divided by a to the power of 6.

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2a
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1 mark

Simplify space p to the power of 2 space end exponent cross times p to the power of 4 space end exponent.

2b
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1 mark

Simplify space m to the power of 15 space end exponent divided by m to the power of 5 space end exponent.

2c
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1 mark

Simplify space open parentheses k cubed close parentheses to the power of 5.

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3a
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1 mark

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

3b
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1 mark

Simplify left parenthesis u to the power of 5 right parenthesis to the power of 5.

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4
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1 mark

t to the power of x cross times t squared equals t to the power of 10
 
Find the value of x.
 

x = ................................................ 

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5
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1 mark

Simplify left parenthesis x to the power of 8 right parenthesis cubed.

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6
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1 mark

Simplify  w squared over w cubed.

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1
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2 marks

Simplify.

2 x to the power of 2 space end exponent cross times space 5 x to the power of 5

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2
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2 marks

Simplify open parentheses 4 x y squared close parentheses cubed.

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3
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2 marks

Simplify open parentheses 5 x to the power of 4 close parentheses cubed.

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4
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2 marks

Simplify 2 x cubed cross times 3 x squared.

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5
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2 marks

3 to the power of negative 2 end exponent cross times 3 to the power of x equals 81

Find the value of x.

 

x = ................................................... 

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6
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2 marks

Simplify.

5 m squared cross times 2 m cubed 

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7
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1 mark

Simplify open parentheses 4 over x close parentheses to the power of negative 2 end exponent space.

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8
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2 marks

Simplify a cubed b to the power of 7 divided by a to the power of 6 b squared.

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9
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2 marks

Simplify  left parenthesis 3 w cubed right parenthesis cubed.

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10
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2 marks

Simplify cube root of 27 t to the power of 27 end root.

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11
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2 marks

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

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12
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2 marks

Simplify space left parenthesis 27 x to the power of 6 right parenthesis to the power of 1 third end exponent.

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13
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2 marks

Simplify left parenthesis 81 y to the power of 16 right parenthesis to the power of 3 over 4 end exponent space.

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14
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2 marks

Simplify.


open parentheses 3 x squared y to the power of 4 close parentheses cubed

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15
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2 marks

Simplify 5 a cubed c squared cross times 2 a squared c to the power of 7.

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16a
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2 marks

Simplify left parenthesis 3 p squared right parenthesis to the power of 5.

16b
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2 marks

Simplify 18 x squared y to the power of 6 divided by 2 x y squared.

16c
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1 mark

Simplify open parentheses 5 over m close parentheses to the power of negative 2 end exponent.

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17
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2 marks

Simplify.

open parentheses 27 x to the power of 9 close parentheses to the power of 2 over 3 end exponent

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18
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3 marks

Simplify.

i)
a cubed cross times a to the power of 6
 
[1]
ii)
left parenthesis 5 x y squared right parenthesis cubed 
 
[2]

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1
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1 mark

25 equals 125 to the power of k

Find the value of k.
 

k equals................................................ 

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2
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3 marks

Simplify open parentheses 256 x to the power of 256 close parentheses to the power of 3 over 8 end exponent.

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3
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2 marks

cube root of y squared end root equals root index 6 of x and space y equals n-th root of x.
 

Find the value of n.
 

n equals................................................. 

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4
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3 marks

Find the value of  left parenthesis 64 x to the power of 4 right parenthesis to the power of 0.5 end exponent space cross times space 4 x to the power of negative 2 end exponent.

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5
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2 marks

Simplify.

open parentheses x cubed over 8 close parentheses to the power of negative 4 over 3 end exponent

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6
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3 marks

x to the power of negative 1 third end exponent equals 32 x to the power of negative 2 end exponent

Find the value of x.

x = ................................................... 

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7
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1 mark

2 cubed equals 4 to the power of p

Find the value of p.
 

p= ............................................ 

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8
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1 mark

Find the value of n when 5 to the power of n equals 1 over 125.
 

n equals.................................................... 

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9
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2 marks

Simplify open parentheses 64 over m cubed close parentheses to the power of negative 1 third end exponent.

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10
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2 marks

      3 to the power of negative q end exponent cross times 1 over 27 equals 81

Find the value of q.

q equals.............................................. 

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11
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2 marks

2 to the power of p equals 1 over 8 to the power of 4

Find the value of p.


p = ............................................ 

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12
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2 marks

Simplify open parentheses fraction numerator 16 a to the power of 8 over denominator c to the power of 12 end fraction close parentheses to the power of 3 over 4 end exponent.

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13
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2 marks

2 to the power of 12 divided by 2 to the power of k over 2 end exponent equals 32

Find the value of k.


k equals ................................................. 

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14
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3 marks

Simplify open parentheses fraction numerator 27 x to the power of 12 over denominator 64 y cubed end fraction close parentheses to the power of negative 1 third end exponent.

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15a
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1 mark

Simplify fully (3e)0

15b
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2 marks

Simplify fully  open parentheses fraction numerator 64 x to the power of 6 over denominator 25 y squared end fraction close parentheses to the power of negative 1 half end exponent

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16
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2 marks

Given that  fraction numerator 7 to the power of 206 cross times 7 to the power of m over denominator 7 to the power of 214 end fraction equals 7 to the power of negative 3 end exponent

find the value of m

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

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17
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1 mark

Given that  open parentheses cube root of 1 over x end root close parentheses to the power of 4 equals x to the power of m

find the value of m

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

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18
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1 mark

Simplify fully  open parentheses fraction numerator 9 t to the power of 4 w to the power of 9 over denominator 18 t to the power of 6 w to the power of 10 end fraction close parentheses to the power of negative 2 end exponent

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19
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4 marks

Given that  4 to the power of k plus 3 space end exponent equals space 16 cross times 2 to the power of k

find the value of k.
Show your working clearly.

k = .................................................. 

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20
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3 marks

Simplify completely      open parentheses fraction numerator 16 w to the power of 8 over denominator y to the power of 20 end fraction close parentheses to the power of begin inline style negative 3 over 4 end style end exponent

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