3√[24x^5 y^3]
3 is the index (the small number in top of the radical sign)

2. $\sqrt[3]{{24x^5 y^3 }} = 2xy\sqrt[3]{{3x^2 }}$

3. Originally Posted by Plato
$\sqrt[3]{{24x^5 y^3 }} = 2xy\sqrt[3]{{3x^2 }}$
Thanks for the help and if you can could you show me the solution

4. Originally Posted by mr_quick
3√[24x^5 y^3]
3 is the index (the small number in top of the radical sign)
$\sqrt[3]{24x^5y^3}=\sqrt[3]{2^3\cdot 3 \cdot x^3 \cdot x^2 \cdot y^3}=2xy \sqrt[3]{3x^2}$
5. $\sqrt[3]{24x^5y^3}=(24x^5y^3)^\frac{1}{3}=24^\frac{1}{3}(x ^5)^\frac{1}{3}(y^3)^\frac{1}{3}$ now there's an exponent rule that says to multiply powers together when you have powers raised to powers so that becomes $2\sqrt[3]{3}x^\frac{5}{3}y$ or $2y(3x^5)^\frac{1}{3}$
$\sqrt[3]{24x^5y^3}=(24x^5y^3)^\frac{1}{3}=24^\frac{1}{3}(x ^5)^\frac{1}{3}(y^3)^\frac{1}{3}$ now there's an exponent rule that says to multiply powers together when you have powers raised to powers so that becomes $2\sqrt[3]{3}x^\frac{5}{3}y$ or $2y(3x^5)^\frac{1}{3}$