Powers, Roots & Standard Form Practice Questions

Write $8.3 \times 10^{5}$ as an ordinary number.

Write $0.00047$ in standard form.

Write $47 \times 10^{3}$ in standard form.

$\sqrt[3]{216}$

$3^{4}$

$\sqrt[4]{625}$

Write $243$ as a power of $3$.

Write $1024$ as a power of $2$.

Write $64$ as a power of $4$.

Write down the name of the object with the smallest diameter.

Write the diameters of the bacterium, the red blood cell and the human hair in order of size.
Start with the smallest diameter.

Work out the difference between the diameter of the grain of sand and the diameter of the human hair.
Give your answer in standard form.

Find the value of $125^{\frac{2}{3}}$.

Find the value of $\left(\dfrac{16}{81}\right)^{-\frac{1}{2}}$.

Work out the value of $7^{0} + 3^{-2}$.
Give your answer as a fraction in its simplest form.

Work out the value of $\left(\dfrac{3}{4}\right)^{-3}$.

Write $(4^{3})^{2} \times 4^{-5}$ as a single power of $4$.

Work out the value of $\dfrac{5^{-2} \times 5^{6}}{5^{8}}$.
Give your answer as a fraction.

Solve $3^{x} = \dfrac{1}{81}$

Solve $8^{x} = 4$

Work out $(4.5 \times 10^{6}) \times (6 \times 10^{-2})$.
Give your answer in standard form.

Work out $(1.44 \times 10^{-3}) \div (3.2 \times 10^{4})$.
Give your answer in standard form.

Work out $(5.6 \times 10^{7}) + (9.3 \times 10^{6})$.
Give your answer in standard form.

Work out $(3.1 \times 10^{-4}) - (8 \times 10^{-5})$.
Give your answer in standard form.

$\sqrt{150}$ lies between two consecutive whole numbers.
Write down these two whole numbers.
You must show how you get your answer.

Show that $\sqrt[4]{700}$ lies between $5$ and $6$.

$$\frac{4^{x} \times 32}{\sqrt{8}} = 2^{9}$$

Work out the exact value of $x$.

Work out the length of one edge of the cube.
Give your answer in standard form.

Work out the total surface area of the cube.
Give your answer in standard form.

Work out the volume of the sheet of foil.
Give your answer in standard form.

The sheet of foil is a square of side $0.5$ m.

Work out the thickness of the sheet of foil.
Give your answer in standard form.