Algebraic Roots & Indices (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

Simplify.

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

Simplify.

$2x^2\times 5x^5$

Simplify ${\left(4x{y}^2\right)}^3$.

Simplify $8t^8÷4t^4$.

Simplify ${\left(5x^4\right)}^3$.

Simplify ${\left(27x^6\right)}^{\frac{1}{3}}$.

Simplify $2x^3\times 3x^2$.

$3^{-2}\times 3^x=81$

Find the value of $x$.

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

Simplify.

i) $a^3\times a^6$  

[1]

ii) ${\left(5x{y}^2\right)}^3$   

[2]

Simplify ${\left(\frac{4}{x}\right)}^{-2}$.

Simplify $a^3{b}^7÷a^6{b}^2$.

Simplify $5a^3{c}^2\times 2a^2{c}^7$.

Simplify  ${\left(3w^3\right)}^3$.

$25={125}^k$

Find the value of $k$.  

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

Simplify  ${\left(27x^9\right)}^{\frac{2}{3}}.$

Find the value of  ${\left(64x^4\right)}^{0.5}\times 4x^{-2}$.

$2^3=4^p$

Find the value of $p.$  

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

Find the value of $n$ when $5^n=\frac{1}{125}$.  

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

Simplify ${\left(\frac{64}{m^3}\right)}^{-\frac{1}{3}}$.

$2^p=\frac{1}{8^4}$

Find the value of $p$.

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

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

find the value of $m$

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

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

$2^{12}÷2^{\frac{k}{2}}=32$

Find the value of $k$.

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

Simplify ${\left(\frac{27x^{12}}{64y^3}\right)}^{-\frac{1}{3}}$.

      $3^{-q}\times \frac{1}{27}=81$

Find the value of $q$.

$q=$.............................................. 

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

Given that  $4^{k+3}=16\times 2^k$

find the value of $k$.

Show your working clearly.

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