Powers & Roots (Edexcel IGCSE Maths A (Modular): Higher Unit 1): Exam Questions

Write down the value of ${10}^0$.

Write down the value of ${10}^{-2}$.

Write down the value of  ${100}^{\frac{1}{2}}$.

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

Write down the value of ${36}^{\frac{1}{2}}$.

Write down the value of ${23}^0$.

Work out the value of ${27}^{-\frac{2}{3}}$.

Write down the value of 10⁰.

Work out the value of 25^-3.

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.

Write ${\left(\sqrt[4]{8}\right)}^5$ as a power of 2.

You are given that $177147=3^{11}$

$3^n=177147\times 9^5$

Find the value of $n.$

Show that $2^{-3}=\frac{1}{8}$

$5\sqrt{5}$ can be written in the form $5^k$.

Find the value of $k$.

Show that ${81}^{-\frac{1}{2}}=\frac{1}{9}$   

Show that ${\left(\frac{64}{125}\right)}^{\frac{2}{3}}=\frac{16}{25}$

Write down the value of ${64}^{\frac{1}{2}}$.

Show that ${\left(\frac{8}{125}\right)}^{-\frac{2}{3}}$ = $\frac{25}{4}$

Show that $\sqrt[3]{8\times {10}^6}$ = 200

Show that ${144}^{\frac{1}{2}}\times {64}^{-\frac{1}{3}}=3$

Solve     $3^{2x}=\frac{1}{81}$.

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.

$a=25\times {10}^{14n}$ where $n$is an integer.

Find an expression, in terms of $n$ , for $a^{\frac{3}{2}}$

Give your answer in standard form.

Show that  $\frac{\sqrt[3]{81}}{3}$ can be written as $3^{\frac{1}{3}}$