Laws of indicesAQA A-Level Maths: Mind map

Exam questions on Laws of indices

1. A student evaluates numerical powers without a calculator, using the laws of indices.
   Evaluate $\left(\dfrac{27}{8}\right)^{-\frac23}$, giving your answer as a fraction in its simplest form.2 marks
2. Throughout this question, $x>0$.
   Solve the equation $x^{-\frac32}=\dfrac18$.2 marks
3. The function $f$ is defined by $f(x)=\dfrac{x^{2}+3x}{\sqrt{x}}$ for $x>0$.
   Write $f(x)$ in the form $x^{p}+kx^{q}$, where $p$, $q$ and $k$ are constants to be found.3 marks