AHL 1.10—Expressions with non-integer exponents Questionbank

Find the value of $a$ and $b$.

Given that $8 \sqrt{2}=2^{a}$, find the value of $a$.

$\frac{\left(4 x y^{-2}\right)\left(-12 x^{-4} y^{12}\right)}{6 x^{2} y}$

$\left(2 x^{-1} y^{-2}\right)^{-3}\left(4 x^{2} y^{3}\right)^{4}$

$\sqrt{\left(9 x^{6} y^{-2} z^{4}\right)^{3}}(3 x y z)^{-2}$

$\left(\frac{x^{2} z^{4}}{2 y^{5}}\right)\left(\frac{3 x^{2} y^{3}}{z^{2}}\right)^{2}$

Find the value of $p$.

Let $a^{\frac{1}{5}} \times a^{\frac{2}{5}}=8$. Find the value of $a$.

$(\sqrt[5]{x})^{6}$

$\sqrt[4]{\sqrt[3]{x}}$

$\frac{1}{\sqrt[3]{x^{4}}}$

$\left(\frac{2}{9} x^{\frac{1}{2}} \times \frac{1}{18} x^{\frac{-3}{4}}\right)^{-\frac{1}{4}}$

$\frac{\left(8 x^{-\frac{2}{3}}\right)^{\frac{2}{3}}}{\left(64 x^{-\frac{1}{3}}\right)^{\frac{1}{3}}}$

$2 x^{-1}-2 x^{-\frac{1}{2}}+\frac{1}{2}$

Show that $\frac{x\left(2 x^{4}-\sqrt{x}\right)}{x^{2}}$ can be written as $2 x^{a}-x^{b}$, where $a$ and $b$ are rational numbers. Find the value of $a$ and $b$.

$\frac{2}{3} x^{\frac{7}{6}} \times \frac{5}{2} x^{\frac{-5}{3}}$

$\left(8 x^{2}\right)^{-\frac{1}{3}} \times \frac{1}{4} x^{-\frac{1}{3}}$

$\left(x^{3} y^{-5}\right)\left(2 x^{-4} y^{2}\right)\left(4 x y^{5}\right)$

$\left(\frac{x}{y^{2}}\right)^{5}\left(x^{2} y^{3}\right)^{3}$

$y^{\frac{3}{4}}$

$y^{-\frac{1}{2}}$

$\left(y^{\frac{1}{2}}\right)^{-3}$