1.10 Rational exponentsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 1.10 Rational exponents

1. Let $p=8^{\frac23}$ and $q=4^{-\frac12}$.
   Write $pq$ as a single power of $2$.2 marks
2. A cube has volume $V$ cm$^3$ and edge length $s$ cm, so that $s=V^{\frac13}$.
   A cube has surface area $150$ cm$^2$. Find its volume.2 marks
3. For $x>0$, consider $A=\frac{x^{\frac32}\times x^{-\frac12}}{\sqrt{x}}$ and $B=\frac{3}{\sqrt[3]{x^{2}}}$.
   Write $A$ in the form $x^{k}$, where $k\in\mathbb{Q}$.3 marks