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SAT Mathematics Practice Test 5

Question : 12 of 58

Marks: +1, -0

9^{\frac{3}{4}}

Solution:

Since 9 can be rewritten as

3^2,9^{\frac{3}{4}}

is equivalent to

3^{2^{\frac{3}{4}}}

. Applying theproperties of exponents, this can be written as

3^{\frac{3}{2}},

which can further be rewritten as

3^{\frac{2}{2}}\left(3^{\frac{1}{2}}\right)

expression that is equivalent to

3\sqrt{3}

Choices A is incorrect; it is equivalent to

9^{\frac{1}{3}}

Choice B is incorrect; it is equivalent to

9^{\frac{1}{4}}

.Choice C is incorrect; it is equivalent to

3^{\frac{1}{2}}

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