### Instruction: Express the following as a common fraction: $\sqrt[3]{4\div 13.5}$.### Response: To express a cube root as a common fraction, I need to find a numerator and denominator that are both perfect cubes.
I can rewrite 4 as $2^2$ and 13.5 as $27 \div 2$.
Then I have $\sqrt[3]{\frac{2^2}{27 \div 2}} = \sqrt[3]{\frac{2^2 \cdot 2}{27}} = \sqrt[3]{\frac{2^3}{27}}$.
Now I can take the cube root of both the numerator and the denominator, and simplify.
I get $\frac{\sqrt[3]{2^3}}{\sqrt[3]{27}} = \frac{2}{3}$.