IGCSEMathsEdexcelMaths A (Modular)Higher Unit 1Exam QuestionsNumberPowers & Roots

Powers & Roots (Edexcel IGCSE Maths A (Modular): Higher Unit 1): Exam Questions

Exam code: 4XMAF/4XMAH

52 mins22 questions
Easy
Medium
Hard
1
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2 marks

Write these numbers in order of size. Start with the smallest number.

5 to the power of negative 1 end exponent

0.5

negative 5

5 to the power of 0

How did you do?

2
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1 mark

Show that 125 to the power of 2 over 3 end exponent is the same as 25

How did you do?

3
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1 mark

Show that 3 to the power of negative 2 end exponent is equal to 1 over 9

How did you do?

4
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1 mark

Write down the reciprocal of 5.

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5
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1 mark

Write 5 to the power of 17 space cross times space 5 squared as a single power of 5 

How did you do?

6a
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1 mark

Write down the value of m, given that  3 to the power of 4 space end exponent cross times space space 3 to the power of 5 space equals space 3 to the power of m

m space equals.................................. 

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6b
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1 mark

Write down the value of n, given that open parentheses 5 cubed close parentheses to the power of 7 equals 5 to the power of n

n space equals.............................

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6c
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2 marks

Find the value of p, given that fraction numerator 7 to the power of 8 cross times 7 squared over denominator 7 to the power of p end fraction equals 7 to the power of 6

p space equals .......................................................

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7
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1 mark

Circle the expression that has the largest value when    a space less than space – 1

1 half a

a

a squared

a cubed

How did you do?

1a
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1 mark

Write down the value of 10 to the power of 0.

How did you do?

1b
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1 mark

Write down the value of 10 to the power of negative 2 end exponent.

How did you do?

2a
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1 mark

Write down the value of  100 to the power of 1 half end exponent.

How did you do?

2b
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2 marks

Find the value of 125 to the power of 2 over 3 end exponent.

How did you do?

3a
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1 mark

Write down the value of 36 to the power of 1 half end exponent.

How did you do?

3b
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1 mark

Write down the value of 23 to the power of 0.

How did you do?

3c
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2 marks

Work out the value of 27 to the power of negative 2 over 3 end exponent.

How did you do?

4
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1 mark

Write down the value of 100.

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5
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1 mark

Work out the value of 25-3.

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6
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1 mark

Patrick has to work out the exact value of 64 to the power of 1 fourth end exponent

Patrick says,

      "1 fourth of 64 is 16 so 64 to the power of 1 fourth end exponent space equals space 16"

Explain what is wrong with what Patrick says.

How did you do?

7
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3 marks

Write open parentheses fourth root of 8 close parentheses to the power of 5 as a power of 2.

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8
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3 marks

You are given that 177147 equals 3 to the power of 11

3 to the power of n equals 177147 space cross times 9 to the power of 5

Find the value of n.

How did you do?

1a
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1 mark

Show that 2 to the power of negative 3 end exponent equals 1 over 8

How did you do?

1b
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1 mark

5 square root of 5 can be written in the form 5 to the power of k.

Find the value of k.

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2a
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2 marks

Show that 81 to the power of negative 1 half end exponent equals 1 over 9   

How did you do?

2b
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2 marks

Show that open parentheses 64 over 125 close parentheses to the power of 2 over 3 end exponent equals 16 over 25

How did you do?

3a
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1 mark

Write down the value of 64 to the power of 1 half end exponent.

How did you do?

3b
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2 marks

Show that open parentheses 8 over 125 close parentheses to the power of negative 2 over 3 end exponent = 25 over 4

How did you do?

4a
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1 mark

Show that cube root of 8 cross times 10 to the power of 6 end root = 200

How did you do?

4b
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2 marks

Show that 144 to the power of 1 half end exponent cross times 64 to the power of negative 1 third end exponent equals 3

How did you do?

4c
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2 marks

Solve     3 to the power of 2 x end exponent space equals fraction numerator space 1 over denominator 81 end fraction.

How did you do?

5
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3 marks

Simplify  8 squared space cross times cube root of 4 to the power of 6 end root

Give your answer in the form 2a where a is an integer.

Show each stage of your working clearly.

How did you do?

6
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3 marks

a space equals space 25 space cross times space 10 to the power of 14 n end exponent where nis an integer.

Find an expression, in terms of n , for a to the power of 3 over 2 end exponent

Give your answer in standard form.

How did you do?

7
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3 marks

Show that  fraction numerator cube root of 81 over denominator 3 end fraction can be written as 3 to the power of 1 third end exponent

How did you do?