Algebraic Roots & Indices (Cambridge International IGCSE Mathematics): Exam Questions

$6^{10}\times6^{x}=6^{2}$

Find the value of $x$.

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

Find the value of $x$ when $5^{x}\times5^{3}=5^{12}$

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

Simplify.

$p^{2}\times p^{4}$

$m^{15}\div m^{5}$

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

$9^{12}\div9^{w}=9^{4}$

Find the value of $w$.

$w=$................................

Simplify $( w^{5} )^{4}$

Simplify.

$t^{21}\div t^{7}$

$( u^{5} )^{5}$

Simplify

$( x^{8} )^{3}$

Simplify.

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

Simplify $( x^{5} )^{2}$.

$x^{3}\times x^{6}=x^{m}$

Find the value of $m$.

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

$( x^{2} )^{n} = x^{12}$

Find the value of $n$.

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

i) $2^{8}\times2^{m}=2^{6}$

Work out the value of $m$.

$m$ = ................................................. [1]

ii) $5^{n}\div5^{4}=5^{6}$ Work out the value of $n$.

$n$ = ................................................. [1]

Simplify.

$5\times x^{0}$

Simplify $2x^{3}\times3x^{2}$

Simplify.

$5m^{2}\times2m^{3}$

(i) Find the value of $k$ when $x^{10}\div x^{k}=x^{3}$.

$k=$....................... [1]

(ii) Find the value of $n$ when $y^{10}\times y^{n}=1$.

$n=$......................... [1]

Simplify.

$4p^{5}q^{3}\times p^{2}q^{-4}$

Simplify $8t^{8}\div4t^{4}.$

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

Simplify

$w^{7}\div w^{-2}$

$4^{w}=\frac{1}{16}$

Find the value of $w$.

$w=$ ...............................