Complicated exponent

GeauxSwish wrote:Problem: (x^-5/x^-9)^1/2.

The answer is x2, but here is my confusion


To do this problem my first instinct was to just flip the fraction in the parenthesis, but someone I've been working with told me that's not possible. There approach was to multiply the denominator by a negative fraction, and then multiply. But I'm still confused as to why his version is right and mine is wrong

GeauxSwish wrote:

Brent@GMATPrepNow wrote:

GeauxSwish wrote:Problem: (x^-5/x^-9)^1/2.

The answer is x2, but here is my confusion


To do this problem my first instinct was to just flip the fraction in the parenthesis, but someone I've been working with told me that's not possible. There approach was to multiply the denominator by a negative fraction, and then multiply. But I'm still confused as to why his version is right and mine is wrong

IMPORTANT RULES
Division Rule: (x^a)/(x^b) = x^(a-b)
Power of a Power Rule: (x^a)^b = x^(ab)

(x^-5/x^-9)^1/2 = (x^(-5 - -9))^1/2 [Division Rule]
= (x^4)^1/2
= x^(4 times 1/2) [Power of a Power Rule]
= x^2

Cheers,
Brent

So if I understand correct my way where I just flip the whole fraction so its x^9/x^5 is just straight up illegal