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Complicated exponent

This topic has 3 expert replies and 1 member reply

Complicated exponent

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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

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GMAT/MBA Expert

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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

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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/x5 is just straight up illegal

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GMAT/MBA Expert

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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
Your way is correct.
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

_________________
Brent Hanneson – Creator of GMATPrepNow.com
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Post
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
That's actually fine!

You should get x⁹ / x⁵, which is the same thing as x⁴. All that's left is to take the square root of x⁴ (since you're raising to the 1/2 power, which is the same thing as taking the root), and you're done!

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