Question

Find the cube root of the following expressions.
a) $\frac{8a^3{b}^6}{1000}$
b) $15\frac{5}{8}{a}^9$

Answer 1

a) $\sqrt[3]{3\frac{8a^3{b}^6}{1000}}=\sqrt[3]{3\frac{2\times 2\times 2\times a\times a\times a\times b\times b\times b\times b\times b\times b}{10\times 10\times 10}}=\frac{2\times a\times b\times b}{10}=\frac{a{b}^2}{5}$

b) $\sqrt[3]{315\frac{5}{8}{a}^9}=\sqrt[3]{3\frac{125}{8}{a}^9}=\sqrt[3]{3\frac{5\times 5\times 5}{2\times 2\times 2}{\left(a^3\right)}^3}=\frac{5a^3}{2}$