Algebraic Roots & Indices (Edexcel IGCSE Maths): Exam Questions

$16^{\frac{1}{5}}\times2^{x}=8^{\frac{3}{4}}$

Work out the exact value of $x$.

Simplify $5u^{2}w^{4}\times7uw^{3}$

Simplify $( m^{- 2} )^{5}$

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

Find the value of $x$.

$( 7^{2} )^{y} = 7^{10}$

Find the value of $y$.

$100^{a}\times1000^{b}$ can be written in the form $10^{w}$

Show that $w=2a+3b$

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

Simplify $m^{5}\div m^{3}$

Simplify $5x^{4}y^{3}\times x^{2}y$

Simplify fully $( 3 e )^{0}$

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

Simplify $a^{4}\times a^{5}$

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

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

Simplify $m^{5}\times m^{3}$

Simplify $\frac{p^{6}}{p^{2}}$

Given that $\frac{7^{206}\times7^{m}}{7^{214}}=7^{-3}$

find the value of $m$

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

Simplify $x^{7}\times x^{3}$

Simplify $( m^{4} )^{3}$

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

Simplify $p^{2}\times p^{5}$

Simplify $g^{6}\div g^{4}$

Simplify $( k^{3} )^{2}$

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

find the value of $m$

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

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

Simplify $t^{8}\div t^{3}$

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

work out the value of $n$.

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

Simplify $( p^{3} )^{2}$

Simplify $\frac{t^{8}}{t^{3}}$

$2^{3}\times2^{n}=2^{9}$

Work out the value of $n$.

$2x^{3}=128$

Work out the value of $x$.

Simplify $( t^{3} )^{2}$

Simplify $\frac{w^{9}}{w^{4}}$

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

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

Write down the value of $g^{0}$

Given that $4^{k+3}=16\times2^{k}$

find the value of $k$.

Show your working clearly.

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

Solve $3x^{2}=147$

Work out the value of $2^{-3}$

Simplify $( 3 x^{2} )^{3}$

$w=4p-16$

Make $p$the subject of this formula.

Simplify $e^{8}\div e^{2}$

Simplify completely $( (16 w ^ 8)/(y ^ 20) ) ^ - 3 / 4$

Simplify $2a^{3}b\times5a^{2}b^{3}$

Simplify $(3x^{2}y)^{0}$

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

find the value of $n$.

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

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

Simplify $\frac{x^{9}}{x^{2}}$

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 $m^{3}\times m^{4}$

Simplify $( 5 n p^{3} )^{3}$

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

Simplify $w^{1}\times w^{0}$

Circle your answer.

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

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

Given that $y^{18}\div y^{6}=y^{k}$ , find the value of $k$.

$k$ = ...................

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

Work out $a$ and $b$

$a=......................\,b=......................$

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

Simplify.

$a^{6}\div a^{2}$

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

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

Simplify.

$( b^{5} )^{3}$

$\sqrt{2}\div\frac{8^{3}}{16^{\frac{3}{2}}}=2^{n}$

Work out the value of $n$. Show your working clearly.

Simplify $( 2 c^{4} d^{7} )^{3}$

Find the value of $5y^{0}$ where $y>0$

Simplify.

$\frac{3y^{3}}{y^{-4}}$

Simplify fully $( 32 a^{15} ) ^{\frac{3}{5}}$

Express $( \frac{1}{10 x} )^{- 3}$ in the form $px^{n}$ where $p$ and $n$ are integers.

Simplify $h^{15}\div h^{3}$

Simplify fully $( 2 g^{3} k^{5} )^{4}$

Given that $\frac{y^{5}\times y^{n}}{y^{7}}=y^{12}$, work out the value of $n$.

$2^{7}\times4^{5}=4^{x}$

Calculate the value of $x$

Simplify fully $( 125 p^{6} y^{24} ) ^{\frac{2}{3}}$