Respuesta :
The expression [tex](\sqrt[6]{x^{5}})^{7}[/tex] expressed in form of a rational exponent gives;
[tex]x^{35/6}[/tex]
A rational exponent is defined as an exponent that is expressed as a fraction.
That means we want to transform the given expression into one with an exponent that is a fraction.
The given expression is;
[tex](\sqrt[6]{x^{5}})^{7}[/tex]
Now, we can see we have a sixth root and the exponent inside the sixth root is 5.
Now, for example, if we have a cube root of say y, it is expressed as; ∛y. However, it can also be expressed as a rational exponent as; [tex]y^{1/3}[/tex]
Because the exponent of y inside the cube root is 1.
Applying that cube root example to our given expression, we can write it as;
[tex](x^{5/6})^{7}[/tex]
From multiplication property of exponents, we multiply both exponents to get;
[tex]x^{35/6}[/tex]
Read more at; https://brainly.com/question/4104949
