Powers & Roots (Edexcel IGCSE Maths): Exam Questions

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

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

Find the value of $k$.

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

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

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

Show that $125^{\frac{2}{3}}$ is the same as 25

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

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

Show that $3^{-2}$ is equal to $\frac{1}{9}$

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

Show that $144^{\frac{1}{2}}\times64^{-\frac{1}{3}}=3$

Solve $3^{2x}=\frac{1}{81}$.

Write down the reciprocal of 5.

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.

Write $5^{17}\times5^{2}$ as a single power of 5

$a=25\times10^{14n}$ where $n$is an integer.

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

Give your answer in standard form.

Write down the value of $m$, given that $3^{4}\times3^{5}=3^{m}$

$m=$..................................

Write down the value of $n$, given that $( 5^{3} )^{7} = 5^{n}$

$n=$.............................

Find the value of $p$, given that $\frac{7^{8}\times7^{2}}{7^{p}}=7^{6}$

$p=$ .......................................................

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

Circle the expression that has the largest value when $a<--1$

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

You are given that $177147=3^{11}$

$3^{n}=177147\times9^{5}$

Find the value of $n.$