Rewrite with rational exponents.

Question

Rewrite with rational exponents. Assume that the radicand of an even root is a positive quantity

 

6√¯x^5 =

Answer 1

 To convert the radical to rational exponents is simply the exponent becomes the numerator, and the order of  root the denominator of the exponents.

 

X^ 5/6

Answer 2

Rewrite the sixth root of x^5 with rational exponents. Assume that the radicand of an even root is a positive quantity.

 

Let's not use that last sentence; then:

 

(x^5)^(1/6) = ((x^6)/x)^(1/6) = ((x^6)^(1/6))/x^(1/6) = |x|/x^(1/6)

and if x < 0 the result will be an imaginary number.

 

But using the last sentence we can say:

 

|x|/x^(1/6) = x/x^(1/6) = x^(5/6), x non-negative.