IGCSEMathsCambridge (CIE)CoreExam QuestionsAlgebra & SequencesAlgebraic Roots & Indices

Algebraic Roots & Indices (Cambridge (CIE) IGCSE Maths: Core): Exam Questions

Exam code: 0580 & 0980

31 mins20 questions
Easy
Medium
Hard
1
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1 mark

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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1 mark

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
1 mark

Simplify.

p squared cross times p to the power of 4

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3b
1 mark

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

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3c
1 mark

open parentheses k cubed close parentheses to the power of 5

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4
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1 mark

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
1 mark

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

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6a
1 mark

Simplify.

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

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6b
1 mark

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

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7
1 mark

Simplify

open parentheses x to the power of 8 close parentheses cubed

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8
1 mark

Simplify.

open parentheses y to the power of 5 close parentheses cubed

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9
1 mark

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

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10a
1 mark

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
1 mark

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

Find the value of n.

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

How did you do?

1
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2 marks

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]

How did you do?

2
1 mark

Simplify.

5 cross times x to the power of 0

[1]

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3
2 marks

Simplify 2 x cubed cross times 3 x squared

How did you do?

4
2 marks

Simplify.

5 m squared cross times 2 m cubed

How did you do?

5
2 marks

(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]

How did you do?

1
2 marks

Simplify.

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

How did you do?

2
2 marks

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

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3
2 marks

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

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4
1 mark

Simplify

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

How did you do?

5
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1 mark

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

Find the value of w.

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

How did you do?