Fractional exponentsIB MYP Maths Extended: Mind map

Exam questions on Fractional exponents

1. Mia is exploring powers of $64$ without a calculator.
   Evaluate $64^{-\frac{5}{6}}$, giving your answer as a fraction.2 marks
2. Kofi is simplifying algebraic expressions in which $x>0$.
   Simplify $\sqrt[3]{x}\div x^{\frac34}$, giving your answer as a single power of $x$.2 marks
3. The orbital period $T$ (in Earth years) of a planet is modelled by $T=r^{\frac{3}{2}}$, where $r$ is the planet's average distance from its star in astronomical units (AU).
   A dwarf planet has $r=25$. Find its orbital period $T$.3 marks