Fractional exponentsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

a^{\frac1n} means?
a^{\frac mn} in terms of roots?
In a^{\frac mn}, what does the denominator n tell you?
In a^{\frac mn}, what does the numerator m tell you?
a^{-\frac mn}=?
64^{\frac13}
8^{\frac23}
16^{\frac34}
25^{-\frac12}
\left(\frac{27}{8}\right)^{-\frac23}
\left(x^{\frac12}\right)^4
x^{\frac23}\times x^{\frac16}
Which order is easiest: root or power first?

Exam questions on Fractional exponents

Mia is exploring powers of $64$ without a calculator.
Evaluate $64^{-\frac{5}{6}}$ , giving your answer as a fraction.2 marks
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).