Edexcel IGCSE Maths

Topic Questions

Powers, Roots & Standard Form

1
Sme Calculator
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

Did this page help you?

2
Sme Calculator
1 mark

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

Did this page help you?

3
Sme Calculator
1 mark

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

Did this page help you?

4a
Sme Calculator
1 mark

Writespace 7.8 cross times 10 to the power of negative 4 end exponent as an ordinary number.

4b
Sme Calculator
1 mark

Write 95 space 600 space 000 as a number in standard form.

Did this page help you?

5
Sme Calculator
2 marks

Work out the value of space left parenthesis 7.5 space cross times 10 to the power of 4 right parenthesis space cross times space left parenthesis 2.5 space cross times space 10 cubed right parenthesis space
Give your answer in standard form.

Did this page help you?

6
Sme Calculator
1 mark

Write 0.000068 in standard form.

Did this page help you?

7a
Sme Calculator
1 mark

Write 0.000423 in standard form.

7b
Sme Calculator
1 mark

Write 4.5 space cross times space 10 to the power of 4 as an ordinary number.

Did this page help you?

8a
Sme Calculator
1 mark

Write space 0.00562 spacein standard form.

8b
Sme Calculator
1 mark

Write 1.452 space cross times space 10 cubed as an ordinary number.

Did this page help you?

9
Sme Calculator
1 mark

Write down the reciprocal of 5.

Did this page help you?

10
Sme Calculator
1 mark

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

Did this page help you?

11a
Sme Calculator
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.................................. 

11b
Sme Calculator
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.............................

11c
Sme Calculator
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 .......................................................

Did this page help you?

12a
Sme Calculator
1 mark

Write 2.46 cross times 10 to the power of 6 as an ordinary number.

12b
Sme Calculator
1 mark

Write 0.000 space 74 in standard form.

Did this page help you?

13
Sme Calculator
1 mark

Circle the number that is written in standard form.

0.9 × 10–3 6 × 100.5 5.2 × 10–4 12 × 107

Did this page help you?

14
Sme Calculator
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

Did this page help you?

15a
Sme Calculator
2 marks

Write these numbers in standard form.

i)
6500

[1]
ii)
0.0584
[1]
15b
Sme Calculator
1 mark

Work out open parentheses 4.2 space cross times 10 to the power of 5 close parentheses cross times open parentheses 1.8 cross times 10 to the power of negative 2 end exponent close parentheses giving your answer in standard form.

Did this page help you?

16a
Sme Calculator
2 marks

A grain of salt weighs 6.48 space cross times space 10 to the power of negative 5 end exponent spacekg on average.

A packet contains 0.35 kg of salt.


Use this information to calculate the number of grains of salt in the packet.

16b
Sme Calculator
1 mark

Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.

Did this page help you?

17
Sme Calculator
4 marks

Tom researches the weights of plant seeds.

  • One poppy seed weighs 3 cross times 10 to the power of negative 4 end exponent grams
  • 250 pumpkin seeds weigh 21 grams.
  • One sesame seed weighs 3.64 cross times 10 to the power of negative 6 end exponent kilograms.

Write the three types of seed in order according to the weight of one seed.
Write the lightest type of seed first.
You must show how you decide.

Did this page help you?

18
Sme Calculator
5 marks

A newborn baby has an approximate mass of 3.5 kilograms.

A human cell has an approximate mass of 2.7 × 10–11 grams.

Use these values to estimate the number of human cells in a newborn baby.
Give your answer in standard form, correct to 2 significant figures.

Did this page help you?

1a
Sme Calculator
1 mark

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

1b
Sme Calculator
1 mark

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

Find the value of k.

Did this page help you?

2a
Sme Calculator
2 marks

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

2b
Sme Calculator
2 marks

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

Did this page help you?

3a
Sme Calculator
1 mark

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

3b
Sme Calculator
2 marks

Show that open parentheses 8 over 125 close parentheses to the power of negative 2 over 3 end exponent25 over 4

Did this page help you?

4a
Sme Calculator
1 mark

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

4b
Sme Calculator
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

4c
Sme Calculator
2 marks

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

Did this page help you?

5a
Sme Calculator
1 mark

Write 640 space 000 space 000 in standard form.

5b
Sme Calculator
2 marks

Work out left parenthesis 3 space cross times space 10 to the power of 7 right parenthesis space divided by space left parenthesis 6 space cross times space 10 to the power of 4 right parenthesis
Give your answer in standard form.

Did this page help you?

6a
Sme Calculator
1 mark

Write 5 space 400 space 000 as a number in standard form.

6b
Sme Calculator
1 mark

Write space 3.2 space cross times space 10 to the power of negative 4 end exponent spaceas an ordinary number.

6c
Sme Calculator
2 marks

The mass of the Sun is 2 cross times space 10 to the power of 30 kg.
The mass of the largest known star is space 315 spacetimes the mass of the Sun.

Work out the mass of this star.
Give your answer in kg in standard form.

Did this page help you?

7a
Sme Calculator
1 mark

Write 7.97 space cross times space 10 to the power of negative 6 end exponent as an ordinary number.

7b
Sme Calculator
2 marks

Work out the value of left parenthesis 2.52 space cross times space 10 to the power of 5 right parenthesis space divided by space left parenthesis 4 space cross times 10 to the power of negative 3 end exponent right parenthesis
Give your answer in standard form.

Did this page help you?

8
Sme Calculator
3 marks

      p squared equals space fraction numerator x minus y over denominator x y end fraction

x equals 8.5 cross times 10 to the power of 9
y equals 4 cross times 10 to the power of 8

Find the value of p.
Give your answer in standard form correct to 2 significant figures.

Did this page help you?

9a
Sme Calculator
2 marks

T space equals space square root of w over d cubed end root

w space equals space 5.6 cross times 10 to the power of negative 5 end exponent
d space space equals space 1.4 cross times 10 to the power of negative 4 end exponent space

Work out the value of T.
Give your answer in standard form correct to 3 significant figures.

9b
Sme Calculator
2 marks

w is increased by 10 percent sign
d is increased by 5 percent sign

Lottie says,
         "The value of T will increase because both w and d are increased."

Lottie is wrong.
Explain why.

Did this page help you?

10a
Sme Calculator
1 mark

Write 8.2 x 105 as an ordinary number.

10b
Sme Calculator
1 mark

Write 0.000 376 in standard form.

10c
Sme Calculator
2 marks

Work out the value of (2.3 x 1012) ÷ (4.6 x 103)
Give your answer in standard form.

Did this page help you?

11
Sme Calculator
2 marks

Work out the value of (3.5 x  106) ÷ (5 x 10-3).
Give your answer in standard form.

Did this page help you?

12
Sme Calculator
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.

Did this page help you?

13
Sme Calculator
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.

Did this page help you?

14
Sme Calculator
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

Did this page help you?

1
Sme Calculator
3 marks

One sheet of paper is  9 space cross times space 10 to the power of negative 3 end exponentcm thick.

Mark wants to put space 500 spacesheets of paper into the paper tray of his printer.
The paper tray is 4 cm deep.

Is the paper tray deep enough for 500 sheets of paper?
You must explain your answer.

Did this page help you?

2
Sme Calculator
2 marks

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

0.038 space cross times space 10 squared 3800 space cross times space 10 to the power of negative 4 end exponent 380 0.38 space cross times space 10 to the power of negative 1 end exponent

Did this page help you?

3a
Sme Calculator
1 mark

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

3b
Sme Calculator
1 mark

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

3c
Sme Calculator
2 marks

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

2.73 space cross times space 10 cubed 27.3 space cross times space 10 to the power of negative 3 end exponent 273 space cross times space 10 squared 0.00273

Did this page help you?

4a
Sme Calculator
1 mark

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

4b
Sme Calculator
2 marks

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

Did this page help you?

5a
Sme Calculator
1 mark

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

5b
Sme Calculator
1 mark

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

5c
Sme Calculator
2 marks

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

Did this page help you?

6a
Sme Calculator
1 mark

The table shows some information about eight planets.

Planet Distance from Earth (km) Mass (kg)
Earth 0 5.97 cross times 10 to the power of 24
Jupiter 6.29 cross times 10 to the power of 8 1.898 cross times 10 to the power of 27
Mars 7.83 cross times 10 to the power of 7 6.42 cross times 10 to the power of 23
Mercury 9.17 cross times 10 to the power of 7 3.302 cross times 10 to the power of 23
Neptune 4.35 space cross times space 10 to the power of 9 1.024 space cross times space 10 to the power of 26
Saturn 1.28 space cross times space 10 to the power of 9 5.68 space cross times space 10 to the power of 26
Uranus 2.72 space cross times space 10 to the power of 9 8.683 space cross times space 10 to the power of 25
Venus 4.14 space cross times space 10 to the power of 7 4.869 space cross times space 10 to the power of 24

Write down the name of the planet with the greatest mass.
6b
Sme Calculator
1 mark

Find the difference between the mass of Venus and the mass of Mercury.

6c
Sme Calculator
2 marks

Nishat says that Neptune is over a hundred times further away from Earth than Venus is.

Is Nishat right?
You must show how you get your answer.

Did this page help you?

7
Sme Calculator
2 marks

Work out left parenthesis 13.8 space cross times space 10 to the power of 7 right parenthesis space cross times space left parenthesis 5.4 cross times 10 to the power of negative 12 end exponent right parenthesis
Give your answer as an ordinary number.

Did this page help you?

8a
Sme Calculator
1 mark

Write down the value of 100.

8b
Sme Calculator
1 mark

Write 6.7 x 10-5 as an ordinary number.

8c
Sme Calculator
2 marks

Work out the value of (3 x 107) x (9 x 106).

Give your answer in standard form.

Did this page help you?

9
Sme Calculator
2 marks

Calculate 9 space cross times 10 to the power of 4 space cross times space 3 space cross times space 10 cubed.
Give your answer in standard form.

Did this page help you?

10
Sme Calculator
2 marks

Work out the value of left parenthesis 9 space cross times 10 to the power of negative 4 end exponent right parenthesis space cross times space left parenthesis 3 space cross times 10 to the power of 7 right parenthesis.
Give your answer in standard form.

Did this page help you?

11a
Sme Calculator
1 mark

Work out the value of 25-3.

11b
Sme Calculator
2 marks

Work out the value of 3503.
Give your answer in standard form.

Did this page help you?

12
Sme Calculator
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.

Did this page help you?

13a
Sme Calculator
2 marks

The table shows information about the surface area of each of the world’s oceans.

Ocean Surface area in
square kilometres
  Pacific 1.56 space cross times space 10 to the power of 8
  Indian 6.86 space cross times space 10 to the power of 7
  Southern 2.03 space cross times space 10 to the power of 7
  Arctic 1.41 space cross times space 10 to the power of 7
  Atlantic 1.06 space cross times space 10 to the power of 8

Work out the difference, in square kilometres, between the surface area of the Atlantic Ocean and the surface area of the Indian Ocean.
Give your answer in standard form.

.......................square kilometres
13b
Sme Calculator
1 mark

The surface area of the Pacific Ocean is k times the surface area of the Arctic Ocean.

Work out the value of k.
Give your answer correct to the nearest whole number.

k space equals...........................

Did this page help you?

14
Sme Calculator
3 marks

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

Did this page help you?

15
Sme Calculator
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.

Did this page help you?

16a
Sme Calculator
2 marks

A company makes sweets.
The sweets are put into packets.

Here are some facts.

bold 1 bold. bold 47 bold space bold cross times bold space bold 10 to the power of bold 7

sweets are made every day

 

bold 3 bold. bold 5 bold space bold cross times bold space bold 10 to the power of bold 5

packets of sweets are 
produced every day

Calculate the mean number of sweets in one packet.

16b
Sme Calculator
3 marks

Sweets are made on 288 days each year.

Calculate the number of sweets made each year.
Give your answer in standard form.

16c
Sme Calculator
4 marks

The company has 152 machines making the sweets.
Each machine operates for 15 hours each day.

i)
Calculate the number of sweets made by one machine each hour.
Give your answer as an ordinary number correct to the nearest 10.

[3]

ii)
State one assumption you have made in part (c)(i).

[1]

Did this page help you?