Algebraic Roots & Indices (OCR GCSE Maths: Higher): Exam Questions

Simplify     $5u^2{w}^4\times 7u{w}^3$

Simplify     ${\left(9x^8{y}^3\right)}^{\frac{1}{2}}$

Simplify       $a^4\times a^5$

Simplify           $\frac{45e^6{f}^8}{5e{f}^2}$

Write down the value of   $9^{\frac{1}{2}}$

Simplify        $x^7\times x^3$

Simplify       ${\left(m^4\right)}^3$

Simplify    $\frac{36a{f}^8}{12a^5{f}^2}$

Simplify      ${\left(3x^2{y}^4\right)}^3$

Simplify      ${\left(p^3\right)}^2$

Simplify     $\frac{t^8}{t^3}$

$2^3\times 2^n=2^9$ Work out the value of $n$.

$2x^3=128$

Work out the value of $x$.

Simplify fully    $\frac{p^3\times p^4}{p^2}$

Solve     $3x^2=147$

Work out the value of $2^{-3}$

Simplify    ${\left(3x^2\right)}^3$

$w=4p-16$

Make $p$the subject of this formula.

Simplify       $2a^{3}b\times 5a^2{b}^3$

Simplify fully    $\frac{n^7\times n^3}{n^6}$

Simplify    $m^3\times m^4$

Simplify     ${\left(5n{p}^3\right)}^3$

Simplify       $\frac{32q^9{r}^4}{4q^{3}r}$

Simplify fully.

$\frac{3a^8\times 2a^5}{a^2}$

Show that $a^5\times {\left(a^3\right)}^2$ can be expressed as $a^{11}$.

Simplify  ${\left(2x^3{y}^5\right)}^4$

Simplify   ${\left(16e^{10}{f}^6\right)}^{\frac{1}{2}}$

${16}^{\frac{1}{5}}\times 2^x=8^{\frac{3}{4}}$

Work out the exact value of $x$.

$p^3\times p^x=p^9$

Find the value of $x$.

${\left(7^2\right)}^y=7^{10}$

Find the value of $y$.

${100}^a\times {1000}^b$ can be written in the form ${10}^w$

Show that $w=2a+3b$

Simplify fully    ${\left(3e\right)}^0$

Simplify fully      ${\left(\frac{64x^6}{25y^2}\right)}^{-\frac{1}{2}}$

Show that $\sqrt[3]{a^4}\times \frac{1}{a}$  can be expressed as $a^{\frac{1}{3}}$.

Simplify.

$4a^{\frac{1}{2}}\times 3a^2$

${\left[\frac{2a^2}{a^{-3}}\right]}^3$

Show that  ${\left(a^3\right)}^{-\frac{1}{3}}\times {\left(a^2\right)}^{\frac{1}{2}}=1$.

Given that  ${\left(\sqrt[3]{\frac{1}{x}}\right)}^4=x^m$

find the value of $m$

m = ................................................. 

Given that  $\frac{7^{206}\times 7^m}{7^{214}}=7^{-3}$

find the value of $m$

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

Simplify completely      ${\left(\frac{16w^8}{y^{20}}\right)}^{-\frac{3}{4}}$

Given that  $n^{\left(-\frac{4}{5}\right)}={\left(\frac{1}{2}\right)}^4$ where $n>0$

find the value of $n$.

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

Given that  $\frac{y^5\times y^n}{y^6}=y^{13}$

work out the value of $n$.

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

Simplify fully  ${\left(\frac{9t^4{w}^9}{18t^6{w}^{10}}\right)}^{-2}$

Given that  $4^{k+3}=16\times 2^k$

find the value of $k$. Show your working clearly.

k = .................................................. 

Write $27\times {\left(3^2\right)}^7$ as a single power of 3.

Write $16\times 8^{2x}$ as a power of 2 in terms of $x$.

The $n$th term of a sequence is  $4(2^n+2^{n-1})$

Circle the expression that is equivalent to $4(2^n+2^{n-1})$

Simplify fully   $\frac{a^3{b}^2}{cd}\times \frac{c}{a{b}^5}$

$\sqrt{6^2+8^2}=\sqrt[3]{125a^3}$

Work out the value of $a$.

${\left(a{r}^b\right)}^4=16r^{20}$  where $a$ and $b$ are positive integers.

Work out $a$ and $b$

$\begin{array}{l}a=......................\\ b=......................\end{array}$