Describe how to transform this into an expression with a rational exponent. Make sure you respond with complete sentences. \sqrt[3]{x^4} ^(5) Thank you !

Question

Describe how to transform this into an expression with a rational exponent. Make sure you respond with complete sentences.


`\sqrt[3]{x^4} ^(5)`
Thank you !

Answer 1

Rational exponent is an exponent that is fractional in form. Let us dissect this one by one.

An n root means that the number or the variable has a power raised 1 / n. For example, if we have a square root of x, this means that x^(1/2).

So in this case since this is cube root, therefore our total variable is raised to the power of 1 / 3.

Since it is also raised to the power of 5, therefore the total power is 5 / 3. This makes the variable in the form:

(x^4)^(5 / 3)

To simplify this further, our variable x is raised also to the power of 4, therefore we multiply the powers. Which simplify this further into:

x^20 / 3

Answer:

x ^ (20 / 3)
or

`x^(20/3)`