Indices Practice Questions

Circle the expression equivalent to $\dfrac{5}{2}p^{-3}$

• $-\dfrac{5}{2p^{3}}$
• $\dfrac{5}{2p^{3}}$
• $\dfrac{2}{5p^{3}}$
• $\dfrac{2p^{3}}{5}$

Simplify fully $\dfrac{20m^{9}}{(2m^{2})^{3}}$

Work out the value of $64^{-\frac{2}{3}}$

Express $\dfrac{x^{4}\times\sqrt[3]{x}}{\sqrt{x}}$ as a single power of $x$.

The rectangle below has sides of length $(2a^{3})^{2}$ and $\dfrac{5}{a^{4}}$.

Work out the area of the rectangle. Give your answer in its simplest form.

Solve $2^{x}\times 8^{\,x-1}=32$

Solve $x^{-\frac{3}{2}}=8$

$p\times\dfrac{\sqrt[3]{p}}{\sqrt[4]{p}}=\sqrt[c]{p^{\,d}}$ where $c$ and $d$ are positive integers.

Work out the least possible values of $c$ and $d$.

$c=$ ______

$d=$ ______

$2^{x^{2}}\times 8^{x}=16$

Work out the possible values of $x$.

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