Question

What is the simplified form of the following expression? assume x doesn’t = 0

Answer 1

The simplified form is
`\frac{\sqrt[5]{810 x^(3)}}{3x}`

Step-by-step explanation:

we need to simplify the value of x in given expression:

`\sqrt[5]{(10x)/(3x^(3))}`

Re- write the above as,

`\sqrt[5]{(10)/(3x^(2))}`

`\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^(2)}}`

Multiply numerator and denominator by
`(\sqrt[5]{3x^(2)})^(4)`

`\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^(2)}} * \frac{(\sqrt[5]{3x^(2)})^(4)}{(\sqrt[5]{3x^(2)})^(4)}`

`\frac{\sqrt[5]{{10}}{\sqrt[5]{(3x^(2)}})^4}{{3x^(2)}}`

`\frac{\sqrt[5]{{10}}{\sqrt[5]{81x^(8)}}}{{3x^(2)}}`

`\frac{x \sqrt[5]{810 x^(3)}}{3x^(2)}`

`\frac{\sqrt[5]{810 x^(3)}}{3x}`

Hence, the simplified form is

`\frac{\sqrt[5]{810 x^(3)}}{3x}`

Answer 2

For this case we must simplify the following expression:

`\sqrt [5] {\frac {10x} {3x ^ 3}}`

We rewrite the expression as:

`\sqrt [5] {\frac {10x} {x * 3x ^ 2}} =`

We eliminate common factors:

`\sqrt [5] {\frac {10} {3x ^ 2}} =\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}}`

We multiply the numerator and denominator:

`(\sqrt [5] {3x ^ 2}) ^ 4:\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}} * \frac {(\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 4} =`

\frac {\ sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {\sqrt [5] {3x ^ 2} * (\sqrt [5] {3x ^ 2} ) ^ 4} =

`\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} =`

`\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} =`

`\frac {\sqrt [5] {10} * x \sqrt [5] {81x ^ 3}} {3x ^ 2} =\\\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}`

Answer:

`\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}`

`\frac {\sqrt [5] {810x ^ 3}} {3x}`