Powers, Roots & Standard Form (Cambridge International IGCSE Mathematics): Exam Questions

Calculate $0.125^{-\frac{2}{3}}$ .

Work out.

$( \frac{125}{27} )^{- \frac{2}{3} }$

Find the value of $( \frac{1}{81} )^{- \frac{3}{4} }$.

Write $2^{-4}$ as a decimal.

Calculate $( 3 \times 10^{- 3} )^{3}$.

Give your answer in standard form.

Calculate the value of $( 2.3 \times 10^{- 3} ) + ( 6.8 \times 10^{- 4} )$. Give your answer in standard form.

Mohsin has 720 apple trees on his farm.

Each apple tree produces 16 boxes of apples each year. One box contains 18 kg of apples.

Calculate the total mass of apples produced by the 720 trees in one year. Give your answer in standard form.

............................................... kg

The table shows some information about eight planets.

Write down the name of the planet with the greatest mass.

Extract:

| Mercury | 9.17 ![cross times] 10^7^ | 3.302 ![cross times] 10^23^ | | Venus | 4.14 ![cross times] 10^7^ | 4.869 ![cross times] 10^24^ |

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

Extract:

| Neptune | 4.35 × 10^9^ km | | Venus | 4.14 × 10^7^ km |

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.

Work out (13.8 $\times$ 10⁷) $\times$ (5.4 $\times$ 10⁻¹²)

Give your answer as an ordinary number.

Write 640 000 000 in standard form.

Work out (3 $\times$ 10⁷) ÷ (6 $\times$ 10⁴) Give your answer in standard form.

Work out the value of 25^-3

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

The table shows the surface area of some countries and their estimated population in 2017.

Find the total surface area of Brunei and the Maldives.

.......................................... km²

Extract:

| Country | Surface area (km^2^) | Estimated population in 2017 | | Brunei | 5.77 × 10^3^ | 433 100 | | China | 9.60 × 10^6^ | 1 388 000 000 | | France | 6.41 × 10^5^ | 67 000 000 | | Maldives | 3.00 × 10^2^ | 374 600 |

The ratio $\mathrm{surface} \mathrm{area} \mathrm{of} \mathrm{the} \mathrm{Maldives}:\mathrm{surface} \mathrm{area} \mathrm{of} \mathrm{China}$ can be written in the form 1 : $n$.

Find the value of $n$.

$n=$ ................................................

Extract:

| Country | Surface area (km^2^) | Estimated population in 2017 | | Brunei | 5.77 × 10^3^ | 433 100 | | China | 9.60 × 10^6^ | 1 388 000 000 | | France | 6.41 × 10^5^ | 67 000 000 | | Maldives | 3.00 × 10^2^ | 374 600 |

Find the surface area of France as a percentage of the surface area of China.

............................................. %

Extract:

Maldives | 3.00 × 10^2^ | 374 600

Find the population density of the Maldives.

[Population density = population ÷ surface area]

...............................people/km²

Find the exact value of $8^{\frac{2}{3}}\times49^{-\frac{1}{2}}$.

$p^{2}=\frac{x-y}{xy}$

$x=8.5\times10^{9}\,y=4\times10^{8}$

Find the value of p.

Give your answer in standard form correct to $2$ significant figures.

$T=\sqrt{\frac{w}{d^{3}}}\,w=5.6\times10^{-5}\,d=1.4\times10^{-4}$

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

Extract:

T = sqrt(w/d^3)

w is increased by 10% d is increased by 5%

Lottie says,

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

Lottie is wrong. Explain why.