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

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

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

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

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

Simplify.

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

Simplify.

$( x^{8 y^{7} ) \div ( x^{-1} } y^{3} )$

Simplify.

$( 27 x^{9} ) ^{\frac{2}{3}}$

Simplify $(81y^{16})^{\frac{3}{4}}.$

Simplify $(3p^{2})^{5}$.

Simplify $18x^{2}y^{6}\div2xy^{2}$.

Simplify $( \frac{5}{m} )^{- 2}$.

Simplify fully

$( 4 x^{3} y ) \div ( 16 x^{2} y^{2} )$

Simplify fully

$( 8 x ^{3} y^{12} ) ^{\frac{2}{3}}$

Simplify.

$( x^{9 y^{6} ) \div ( x^{-2} } y^{3} )$

Simplify.

$( \frac{x^{3}}{8} )^{- \frac{4}{3} }$

Simplify $\sqrt[3]{27 t^{27} }$.

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

Simplify $( 256 x^{256} ) ^{\frac{3}{8}}$.

cbrt( y ^2 ) = sqrt index 6 of x and space y equals n-th root of x.

Find the value of $n$.

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

$x^{-\frac{1}{3}}=32x^{-2}$

Find the value of $x$.

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

Simplify ( (16 a ^ 8)/(c ^ 12) ) ^ 3 / 4.

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

find the value of $m$

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