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

$2^{3x+1}=8^{2-x}$

Find the value of $x$

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

Simplify.

$\left(x^8{y}^7\right)÷\left(x^{-1}{y}^3\right)$

Simplify.

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

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

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

Simplify $18x^2{y}^6÷2x{y}^2$.

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

Simplify.

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

Simplify $\sqrt[3]{27t^{27}}$.

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

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

$\sqrt[3]{y^2}=\sqrt[6]{x}$ and $y=\sqrt[n]{x}$.  

Find the value of $n$.  

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

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

Find the value of $x$.

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

Simplify ${\left(\frac{16a^8}{c^{12}}\right)}^{\frac{3}{4}}$.

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

find the value of $m$

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