1.10 Rational exponentsIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What is a^{\frac1n}?
What is a^{\frac mn}?
What is x^{-\frac12}?
What does a negative index do?
Simplify 5^{\frac12}\times5^{\frac13}.
Simplify 6^{\frac34}\div6^{\frac12}.
Evaluate 32^{\frac35}.
Evaluate 8^{\frac23}.
Evaluate 4^{-\frac12}.
State the power of a power law.
How do you solve x^{\frac23}=9?
Write \frac{3}{\sqrt[3]{x^{2}}} as a power of x.

Exam questions on 1.10 Rational exponents

Let $p=8^{\frac23}$ and $q=4^{-\frac12}$ .
Write $pq$ as a single power of $2$ .2 marks
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
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

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).