Question

Question 4Rewrite in simplest radical formShow each step of your process.26

Answer 1

The question is given to be:

`\frac{x^{(5)/(6)}}{x^{(1)/(6)}}`

Recall the exponent rule given to be:

`(a^m)/(a^n)=a^(m-n)`

Therefore, we can simplify the expression to be:

`\frac{x^{(5)/(6)}}{x^{(1)/(6)}}=x^{(5)/(6)-(1)/(6)}`

Simplifying the exponent, we have:

`x^{(5)/(6)-(1)/(6)}=x^{(4)/(6)}=x^{(2)/(3)}`

To write in radical form, apply the rule given to be:

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

Therefore, the answer becomes:

`\Rightarrow(\sqrt[3]{x})^2`

ANSWER

`\frac{x^{(5)/(6)}}{x^{(1)/(6)}}=(\sqrt[3]{x})^2`