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
Complicated exponent
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IMPORTANT RULESGeauxSwish 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
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
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So if I understand correct my way where I just flip the whole fraction so its x^9/x5 is just straight up illegalBrent@GMATPrepNow wrote:IMPORTANT RULESGeauxSwish 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
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
GMAT/MBA Expert
- Brent@GMATPrepNow
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Your way is correct.GeauxSwish wrote:So if I understand correct my way where I just flip the whole fraction so its x^9/x^5 is just straight up illegalBrent@GMATPrepNow wrote:IMPORTANT RULESGeauxSwish 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
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
x^(-5) = 1/(x^5) and x^(-9) = 1/(x^9)
So, (x^-5/x^-9) = [1/(x^5)]/[1/(x^9)]
= [1/(x^5)]/[(x^9)/1]
= x^9/x^5
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That's actually fine!GeauxSwish wrote: So if I understand correct my way where I just flip the whole fraction so its x^9/x5 is just straight up illegal
You should get x� / x�, which is the same thing as x�. All that's left is to take the square root of x� (since you're raising to the 1/2 power, which is the same thing as taking the root), and you're done!