Question

How to transform into an expression with a rational exponent

Answer 1

Given the expression:

`(\sqrt[6]{x^5})^7`

Let's transform the expression into an expression with rational exponents.

To transform into an expression with rational exponents, apply the formula:

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

Thus, we have:

`(\sqrt[6]{x^5})^7=(x^{(5)/(6)})^7`

Now, apply the power rule and multiply the exponents:

`\begin{gathered} x^{(5)/(6)*7}=x^{(5*7)/(6)} \\ \\ =x^{(35)/(6)} \end{gathered}`

Therefore, the expression written with rational exponents is:

`x^{(35)/(6)}`

ANSWER:

`x^{(35)/(6)}`