Laws of indices and surdsEdexcel International A Level Maths: Mind map

Exam questions on Laws of indices and surds

1. The number $N=16^{\frac34}\times27^{-\frac23}$.
   Hence find the exact value of $N^{-\frac12}$, giving your answer in the form $k\sqrt2$.2 marks
2. For $x>0$, $f(x)=\dfrac{(2x^3)^2\sqrt{x}}{8x^5}$.
   Solve $f(x)=108$.2 marks
3. A rectangle has area $(7+\sqrt5)$ cm$^2$ and length $(3-\sqrt5)$ cm.
   Find the width of the rectangle, giving your answer in the form $\frac{p+q\sqrt5}{r}$, where $p$, $q$ and $r$ are integers.3 marks