What is the value of $9 ^ { \frac { 1 } { 4 } } \times 3 ^ { - \frac { 1 } { 2 } }$? [2 points]
(1) 1
(2) $\sqrt { 3 }$
(3) 3
(4) $3 \sqrt { 3 }$
(5) 9

102. If $A = \sqrt[6]{4\sqrt[3]{16}}\left(\dfrac{1}{2}\right)^{-\frac{1}{3}}$, then $(2A)^{-\frac{4}{3}}$ equals which of the following?
(1) $0.25$ (2) $0.5$ (3) $0.75$ (4) $1$

If $x = 1 + \sqrt[5]{2} + \sqrt[5]{4} + \sqrt[5]{8} + \sqrt[5]{16}$, then the value of $\left(1 + \frac{1}{x}\right)^{30}$ is
(A) 2
(B) 5
(C) 32
(D) 64

$10 ^ { -1 } + 10 ^ { -2 } + 10 ^ { -3 }$
What is the result of this operation?
A) 0,011
B) 0,101
C) 0,111
D) 0,123
E) 0,321

$15 ^ { 13 } + 6 \cdot 15 ^ { 13 } + 8 \cdot 15 ^ { 13 }$
What is the result of this operation?
A) $15 ^ { 15 }$
B) $15 ^ { 14 }$
C) $14 \cdot 15 ^ { 13 }$
D) $10 \cdot 16 ^ { 13 }$
E) $16 ^ { 13 }$

$\frac { 4 ^ { \frac { 1 } { 2 } } + ( - 8 ) ^ { \frac { 1 } { 3 } } - 1 } { 2 ^ { - 1 } }$
What is the result of this operation?
A) 2 B) 6 C) $-1$ D) 0 E) $-2$

Given that $x = \sqrt [ 4 ] { 5 }$,
$$\left( x ^ { 2 } - 2 \right) ^ { - 1 }$$
which of the following is this expression equal to?
A) $1 + \sqrt [ 4 ] { 5 }$
B) $2 + \sqrt [ 4 ] { 5 }$
C) $1 + \sqrt { 5 }$
D) $2 + \sqrt { 5 }$
E) $1 + 2 \sqrt { 5 }$

$$\frac { 6 ^ { -2 } - 4 \cdot 6 ^ { -3 } } { 3 ^ { -2 } - 2 \cdot 3 ^ { -3 } }$$
What is the result of this operation?
A) $\frac { 1 } { 3 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 1 } { 4 }$

$$\left[ \left( \frac { - 1 } { 2 } \right) ^ { - 2 } \right] ^ { 3 }$$
What is the result of this operation?
A) - 32
B) - 16
C) 12
D) 32
E) 64

$6 ^ { - 3 } \left( 8 ^ { 3 } - 6 ^ { 3 } + 4 ^ { 3 } \right)$ What is the result of this operation?
A) $\frac { 1 } { 2 }$
B) $\frac { 4 } { 3 }$
C) $\frac { 5 } { 3 }$
D) $\frac { 9 } { 4 }$
E) $\frac { 5 } { 6 }$

$$3 ^ { 2 } \cdot \frac { 1 - 3 ^ { - 4 } } { 1 - 3 ^ { - 2 } }$$
What is the result of this operation?
A) 4
B) 5
C) 8
D) 9
E) 10

$$\frac { 6 ^ { -8 } \cdot 9 ^ { 4 } } { 4 ^ { -6 } }$$
What is the result of this operation?
A) 8
B) 9
C) 12
D) 16
E) 18

While teaching the topic of exponents, Teacher Kerem stated that the expression $a^{b^{c}}$ cannot be written without parentheses in this way, because the expressions $a^{\left(b^{c}\right)}$ and $\left(a^{b}\right)^{c}$ can have different values, and explained this situation with an example.
Accordingly, which of the following could be the example given by Teacher Kerem?
A) $a = 1, b = 2, c = 3$ B) $a = 2, \quad b = 1, \quad c = 3$ C) $a = 2, \quad b = 2, \quad c = 2$ D) $a = 3, \quad b = 0, \quad c = 3$ E) $a = 3, \quad b = 2, \quad c = 1$