Indices (AQA GCSE Further Maths): Exam Questions

Solve    $x^{-\frac{2}{3}}=12\frac{1}{4}$

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

$a$ is a value greater than 1

Work out the value of $m$ for which   ${\left(a^m\right)}^4={\left(a^5\right)}^{2m}$

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

$w^3{x}^2{y}^5=w^{13}{x}^7$ Write $y$ in terms of $w$ and $x$. Give your answer in its simplest form.

$y=..................$

Solve   $\sqrt[3]{\left(2\sqrt{x}-10\right)}=2$

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

Write $\sqrt[4]{a\times a^{-9}}$  as an integer power of $a$.

The curve $y=2\sqrt{x-a}+5$passes through the point (1, 8)

Work out the value of $a$.

Work out the value of ${\left(\begin{array}{cc}{3}^{\frac{1}{2}}+& 3^{\frac{3}{2}}\end{array}\right)}^2$

You must show your working.

Solve   ${\left(3-\sqrt{x}\right)}^{\frac{1}{3}}=-2$

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

$\sqrt[4]{x}=2$   and  $y^{-2}=25$

$x>0$ and $y<0$

Work out the value of $\frac{x}{y}$

Solve   $8^x=\frac{2^{56}-4^{26}}{30}$

Work out the value of $p$ when

$9^{0.5p}\times 81={27}^{2p–1}$

Solve $\sqrt{x}-\frac{12}{\sqrt{x}}=1$ where $x>0$