For this case we must simplify the following expression:
[tex]\sqrt [5] {\frac {10x} {3x ^ 3}}[/tex]
We rewrite the expression as:
[tex]\sqrt [5] {\frac {10x} {x * 3x ^ 2}} =[/tex]
We eliminate common factors:
[tex]\sqrt [5] {\frac {10} {3x ^ 2}} =\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}}[/tex]
We multiply the numerator and denominator:
[tex](\sqrt [5] {3x ^ 2}) ^ 4:\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}} * \frac {(\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 4} =[/tex]
\frac {\ sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {\sqrt [5] {3x ^ 2} * (\sqrt [5] {3x ^ 2} ) ^ 4} =
[tex]\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 5} =\\\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {3x ^ 2} =[/tex]
[tex]\frac {\sqrt [5] {10} * \sqrt [5] {(3x ^ 2) ^ 4}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 8}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 5 * x ^ 3}} {3x ^ 2} =[/tex]
[tex]\frac {\sqrt [5] {10} * x \sqrt [5] {81x ^ 3}} {3x ^ 2} =\\\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]
Answer:
[tex]\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]
[tex]\frac {\sqrt [5] {810x ^ 3}} {3x}[/tex]
