Powers, Roots & Standard Form (Edexcel GCSE Maths: Foundation): Exam Questions

i) Write $9.314\times {10}^5$ as an ordinary number.

[1]

ii) Calculate $\left(4.1\times {10}^{-3}\right)\times \left(8.9\times {10}^7\right)$
Give your answer in standard form.

[2]

Find the value of

i) $3^0,$

[1]

ii) $5^{-2}.$

[1]

Write the number 0.0605 in standard form.

Calculate $\left(1.63\times {10}^{12}\right)\times \left(2.47\times {10}^{-1}\right)$

Give your answer in standard form.

Write 45000 in standard form.

Write $2.06\times {10}^{-2}$ as an ordinary number.

[1]

i) Write down the reciprocal of 15.

[1]

ii) Write down the value of ${15}^0$.

[1]

iii) Write 0.015 in standard form.

[1]

Find the value of $6^0+6^2$

Find the value of 5^-3

i) Write $4.2\times {10}^{-3}$ as an ordinary number.

[1]

ii) Calculate $\left(8.1\times {10}^3\right)+\left(7.9\times {10}^4\right)$ Give your answer in standard form.

[2]

Find the value of

i) $\sqrt[3]{512}$

[1]

ii) $\frac{6^8}{2^6}$

[1]

iii) 7⁰

[1]

Work out ${\left(-4\right)}^3$

Find the value of ${\left(\sqrt{25}\right)}^2$.

The mass of the earth is $5.97\times {10}^{24}\mathrm{kg}$.
The mass of Mars is 0.11 times the mass of the earth.

Work out an estimate for the mass of Mars.
Give your answer in standard form.

Explain whether your answer to (a) is an underestimate or an overestimate.

(i) Write «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics»«mrow»«msup»«mn»3«/mn»«mn»4«/mn»«/msup»«mo»§#215;«/mo»«msup»«mn»3«/mn»«mn»3«/mn»«/msup»«/mrow»«annotation encoding=¨application/vnd.wiris.mtweb-params+json¨»{¨fontFamily¨:¨Times New Roman¨,¨fontSize¨:¨18¨,¨autoformat¨:true,¨toolbar¨:¨«toolbar ref=`general`»«tab ref=`general`»«removeItem ref=`setColor`/»«removeItem ref=`bold`/»«removeItem ref=`italic`/»«removeItem ref=`autoItalic`/»«removeItem ref=`setUnicode`/»«removeItem ref=`mtext` /»«removeItem ref=`rtl`/»«removeItem ref=`forceLigature`/»«removeItem ref=`setFontFamily` /»«removeItem ref=`setFontSize`/»«/tab»«/toolbar»¨}«/annotation»«/semantics»«/math» in the form $3^n$

(ii) Write down the value of $3^{-1}$

Write $\frac{7^8\times 7^4}{7^3}$ in the form $7^n$ where $n$ is an integer

The same number is missing from each box.

Find the missing number.

Work out $3^5$

A fan spins at 1200 revolutions per minute.

Calculate the number of revolutions in 3.5 hours.

Write your answer in standard form.

.......... revolutions

Write $3.57\times {10}^{-4}$ as an ordinary number.

Write $8390000$ in standard form.

i) Write $4.81\times {10}^{-3}$ as an ordinary number.

[1]

ii) Write 75000 in standard form.

[1]

iii) Calculate  $\frac{6.3\times {10}^2}{7\times {10}^{-3}}$

Write your answer in standard form.

[2]

Find the value of $x$ when $5^x\times 5^3=5^{12}$

$x=$...........................

The average distance from Earth to Mars is $2.25\times {10}^8$ km. A space ship travels from Earth to Mars at an average speed of $5.8\times {10}^4$ km/h.

Find how long, in hours, the journey takes.

.............................. hours

Find the value of  $p$ when  $5^p÷5^8=5^{13}$.

$p=$....................... 

Mercury is 58 000 000 km from the sun.

Jupiter is 7.22×10⁸ km further from the sun than Mercury.

Earth is 1.5×10⁸ km from the sun. 

Find how many times further from the sun Jupiter is, than Earth.