Question

turn from radical form to exponential expression in rationak form, then multiply and simplify (no need to evaluate) just be put in simplest form and I also need the LCD and I dont know what it is so if you could explain a little how to do everything step by step

Answer 1

Remember that using radical notation, fractionary exponents can be represented as follows:

`a^{(n)/(m)}=\sqrt[m]{a^n}`

On the other hand, when the index of a radical does not appear, we understand that it is equal to 2:

`\sqrt[]{a}=\sqrt[2]{a}`

Rewrite each of the radical factors of the given expression using fractionary exponents:

`\sqrt[5]{x^3}\cdot\sqrt[]{x^4}=x^{(3)/(5)}\cdot x^{(4)/(2)}`

To simplify the expression, use the following rule of exponents:

`a^n* a^m=a^(n+m)`

Then:

`x^{(3)/(5)}\cdot x^{(4)/(2)}=x^{(3)/(5)+(4)/(2)}`

To simplify the expression, solve the addition with fractions:

`(3)/(5)+(4)/(2)`

Simplify the fraction 4/2 as 2/1:

`(3)/(5)+(4)/(2)=(3)/(5)+(2)/(1)`

The leas common denominator for these fractions is 5. Rewrite 2/1 as 10/5 and add the fractions:

`(3)/(5)+(2)/(1)=(3)/(5)+(10)/(5)=(13)/(5)`

Then:

`x^{(3)/(5)+(4)/(2)}=x^{(13)/(5)}`

Therefore, the final expression in rational form, is:

`\sqrt[5]{x^3}\cdot\sqrt[]{x^4}=x^{(13)/(5)}`