IGCSEMathsCambridge (CIE)ExtendedExam QuestionsAlgebra & SequencesAlgebraic Roots & Indices

Algebraic Roots & Indices (Cambridge (CIE) IGCSE Maths: Extended)

Exam Questions

2 hours47 questions

Select a question set to download for
Algebraic Roots & Indices

Select an answer set to view for
Algebraic Roots & Indices

Easy
Medium
Hard
Very Hard
1
Sme Calculator1 mark

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

How did you do?

Did this page help you?

2a
Sme Calculator1 mark

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

How did you do?

2b
Sme Calculator1 mark

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

How did you do?

2c
Sme Calculator1 mark

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

How did you do?

Did this page help you?

3
Sme Calculator2 marks

Simplify.

5 m squared cross times 2 m cubed 

How did you do?

Did this page help you?

1
Sme Calculator2 marks

Simplify.

open parentheses x to the power of 8 y to the power of 7 close parentheses space divided by space open parentheses x to the power of negative 1 end exponent y cubed close parentheses

How did you do?

Did this page help you?

2
Sme Calculator2 marks

Simplify.

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

How did you do?

Did this page help you?

3
Sme Calculator2 marks

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

How did you do?

Did this page help you?

4a
Sme Calculator2 marks

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

How did you do?

4b
Sme Calculator2 marks

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

How did you do?

4c
Sme Calculator1 mark

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

How did you do?

Did this page help you?

1
Sme Calculator2 marks

Simplify.

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

How did you do?

Did this page help you?

2
Sme Calculator2 marks

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

How did you do?

Did this page help you?

3
Sme Calculator3 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

How did you do?

Did this page help you?

1
Sme Calculator3 marks

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

How did you do?

Did this page help you?

2
Sme Calculator2 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................................................. 

How did you do?

Did this page help you?

3
Sme Calculator3 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 = ................................................... 

How did you do?

Did this page help you?

4
Sme Calculator2 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.

How did you do?

Did this page help you?

5
Sme Calculator2 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 = ................................................

How did you do?

Did this page help you?