SAT Mathematics Practice Test 7

Question : 11 of 59

Marks: +1, -0

The expression

{x^{-2}y^{1/2}}/{x^{1/3}y^{-1}}

where x > 1 and y > 1, is equivalent to which of the following?

Solution:

For x > 1and y > 1,

x^{1/3}

and

y^{1/2}

are equivalent to

^3√x

and

√y

, respectively. Also

x^{-2}

and

y^{-1}

are equivalent to

1/{x^2}

and

1/y

respectively. Using these equivalences, the given expression can be rewritten as

{y√y}/{{x^2}\;\;^3√x}

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