Algebraic Roots & Indices Practice Questions

Simplify $w^5 \times w^7$

Simplify $\dfrac{c^{12}}{c^4}$

$\dfrac{k^{12}}{k^{x}} = k^{5}$

Find the value of $x$.

Simplify $(3a^2b^5)^3$

Simplify fully $\dfrac{15p^5q^3}{45p^2q^3}$

Write $3^{-4}$ as a fraction.

Work out the value of $\left(\dfrac{2}{5}\right)^{-2}$

Give your answer as a fraction in its simplest form.

Write down the value of $49^{\frac{1}{2}}$

Work out the value of $27^{\frac{2}{3}}$

Solve $2^{x} \times 8 = 4^{5}$

Solve $\dfrac{125^{n}}{5} = 5^{8}$

Work out the value of $125^{-\frac{2}{3}}$

Work out the value of $\left(\dfrac{16}{81}\right)^{-\frac{3}{4}}$

Simplify $\sqrt{36x^{10}y^{4}}$

Simplify $\sqrt[3]{64p^{9}}$

Simplify fully $\dfrac{6a^{\frac{1}{2}} \times 2a^{\frac{3}{2}}}{3a^{-1}}$

Simplify fully $\left(9x^{-6}\right)^{\frac{1}{2}}$

Show that $\dfrac{8^{x} \times 2^{5}}{16^{x-1}}$ can be written as $2^{9-x}$

Hence solve $\dfrac{8^{x} \times 2^{5}}{16^{x-1}} = 32$

Simplify fully $\left(\dfrac{25x^{6}}{y^{4}}\right)^{-\frac{3}{2}}$

Solve $\sqrt{5} \times 25^{x} = 5^{7}$