Powers, Roots & Standard Form (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

Work out, giving your answer in standard form,

(5.2 × 10⁷) + (5.2 × 10⁶) .

Work out $\left(3\times {10}^{199}\right)+\left(2\times {10}^{201}\right).$

Give your answer in standard form.

Work out  $(6.4\times {10}^7)+(9.6\times {10}^6)$.
Give your answer in standard form.

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

$0.038\times {10}^{2}3800\times {10}^{-4}3800.38\times {10}^{-1}$

Work out the value of (9 $\times$ 10^-4) $\times$ (3 $\times$ 10⁷)

Give your answer in standard form.

Patrick has to work out the exact value of ${64}^{\frac{1}{4}}$

Patrick says,

″$\frac{1}{4}$ of 64 is 16 so ${64}^{\frac{1}{4}}$ = 16"

Explain what is wrong with what Patrick says.

Find the value of ${64}^{\frac{2}{3}}$.

Calculate  $0.{125}^{-\frac{2}{3}}$ .

Work out

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

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

Write 5400 000 as a number in standard form.

Write 3.2 $\times$ 10^-4 as an ordinary number.

The mass of the Sun is 2 $\times$ 10³⁰ kg.
The mass of the largest known star is 315 times the mass of the Sun.

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

Simplify  $8^2\times \sqrt[3]{4^6}$

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

Show each stage of your working clearly.

Work out, giving your answer in standard form,

(7.1 × 10^–15) × (2 × 10³)

Write 0.0017 in standard form.

Work out giving your answer in standard form

$\left(6.3\times {10}^4\right)+\left(3.2\times {10}^3\right)$

Find the value of ${27}^{-\frac{2}{3}}$