Question

Describe how to transform the expression in the photo into an expression with a rational exponent. Please use complete sentences

Answer 1

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

Step 1:

Use the definition of a radical:

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

Step 2:

Use the following property of exponents:

`(x^y)^z=x^(y\cdot z)`

so:

`(x^{(5)/(6)})^7=x^{(5)/(6)\cdot7}=x^{(35)/(6)}`