Question

Simplify ^3sqrt27x^15y^24

Answer 1

the answer is much simpler than the other user might think

remember that $\sqrt[n]{x^m}=x^\frac{m}{n}$

and $\sqrt{ab}=(\sqrt{a})(\sqrt{b})$

so

$\sqrt[3]{27x^{15}y^{24}}=$

$(\sqrt[3]{27})(\sqrt[3]{x^{15}})(\sqrt[3]{y^{24}})=$

factor them all. if they're factored already, then great

$(\sqrt[3]{3^3})(\sqrt[3]{x^{15}})(\sqrt[3]{y^{24}})=$

convert into fractional exponents

$(3^\frac{3}{3})(x^\frac{15}{3})(y^\frac{24}{3})=$

$(3^1)(x^5)(y^8)=$

$3x^5y^8$