SAT Mathematics Practice Test 3

By definition, a

m

n

=n√am for any positive integers m and n .
It follows, therefore ,that a

2

3

=3√a2
Choice A is incorrect.
By definition a

1

n

=n√a for any positive integer n.
Applying this definition as well as the power property of exponents to the expression √a

1

3

yields √a

1

3

=(a

1

3

)

1

2

.Because a

1

6

≠a

2

3

,√a

1

3

is not the correct answer.
Choice B is incorrect.
By definition,a

1

n

=n√a for any positive integer n.
Applying this definition as well as the power property of exponents to the expression √a3 yields √a3=(a3)

1

2

=a

3

2

.
Because a

3

2

≠a

2

3

,√a3 is not the correct answer.
Choice C is incorrect.
By definition, a

1

n

=√a for any positive integer n.
Applying this definition as well as the power property of exponents to the expression 3√a

1

2

yields 3√a

1

2

=(a

1

2

)

1

3

=a

1

6

Because a

1

6

≠a

2

3

,3√a

1

2

is not the correct answer.