Powers, Roots & Standard Form (Cambridge (CIE) O Level Maths): Exam Questions

Here are some numbers written in standard form

$3.4\times {10}^{-1}$       $1.36\times {10}^6$       $7.9\times {10}^0$       $2.4\times {10}^5$       $5.21\times {10}^{-3}$       $4.3\times {10}^{-2}$

From these numbers, write down;

i) the largest number,  

[1]

ii) the smallest number.

[1]

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

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

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.

The table shows information about the annual coffee production of some countries in a recent year.

In the same year, Brazil produced $48$ million bags of coffee.

Complete the table with the coffee production for Brazil, using standard form. 

How many more bags of coffee were produced in Vietnam than in Colombia?

The mass of a bag of coffee is$60$ kg.

Work out the number of kilograms of coffee produced in Indonesia. Give your answer in standard form

Evaluate ${\left(\frac{5}{3}\right)}^{-2}$

Estimate, correct to the nearest whole number, the value of $\sqrt{97}-\sqrt{35}$. Show clearly the approximate values you use.

Write ${27}^{-\frac{4}{3}}$ as a fraction in its simplest form.

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

Work out, giving your answer in standard form,

(5.2 × 10⁷) + (5.2 × 10⁶) .

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

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.

Work out the value of (9 $\times$ 10^-4) $\times$ (3 $\times$ 10⁷)
Give your answer in standard form.

Write ${25}^{-\frac{3}{2}}$ as a a fraction in its simplest form.

$a=\frac{b^2+c}{d}$

i) Find a when $b=4\times {10}^2$ , $c=6\times {10}^3$and $d=2\times {10}^2$ .
Write your answer in standard form.

$a$ = .................................................

ii) Rearrange the formula to make b the subject.

$b$ = .................................................

$m\times {10}^4+m\times {10}^2=36360$

Work out  $m\times {10}^4-m\times {10}^2$

Work out, giving your answer in standard form,

(7.1 × 10^–15) × (2 × 10³)

Work out $\left(3\times {10}^{199}\right)+\left(2\times {10}^{201}\right).$
Give your answer in standard form.

Calculate  $0.{125}^{-\frac{2}{3}}$ .

Work out.

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

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

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.