Among other research objects, Allometry studies the relationship between measurements of different parts of the human body. For example, according to Allometry, the area A of the body surface of a person relates to their mass $m$ by the formula $A = k \cdot \mathrm{~m}^{\frac{2}{3}}$, where $k$ is a positive constant.
If during the period from childhood to adulthood of an individual their mass is multiplied by 8, by how much will the area of body surface be multiplied?
(A) $\sqrt[3]{16}$
(B) 4
(C) $\sqrt{24}$
(D) 8
(E) 64

QUESTION 170
The value of $2^{10}$ is
(A) 512
(B) 1024
(C) 2048
(D) 4096
(E) 8192

The value of $2^{10}$ is:
(A) 512
(B) 1024
(C) 2048
(D) 4096
(E) 8192

What is the value of $3 ^ { \frac { 2 } { 3 } } \times 9 ^ { \frac { 3 } { 2 } } \div 27 ^ { \frac { 8 } { 9 } }$? [2 points]
(1) 1
(2) $\sqrt { 3 }$
(3) 3
(4) $3 \sqrt { 3 }$
(5) 9

What is the value of $3 ^ { \frac { 2 } { 3 } } \times 9 ^ { \frac { 3 } { 2 } } \div 27 ^ { \frac { 8 } { 9 } }$? [2 points]
(1) 1
(2) $\sqrt { 3 }$
(3) 3
(4) $3 \sqrt { 3 }$
(5) 9

What is the value of $5 ^ { \frac { 2 } { 3 } } \times 25 ^ { - \frac { 5 } { 6 } }$? [2 points]
(1) $\frac { 1 } { 25 }$
(2) $\frac { 1 } { 5 }$
(3) 1
(4) 5
(5) 25

What is the value of $5 ^ { \frac { 2 } { 3 } } \times 25 ^ { - \frac { 5 } { 6 } }$? [2 points]
(1) $\frac { 1 } { 25 }$
(2) $\frac { 1 } { 5 }$
(3) 1
(4) 5
(5) 25

When $a = \sqrt { 2 } , b ^ { 3 } = \sqrt { 3 }$, what is the value of $( a b ) ^ { 2 }$? (Here, $b$ is a real number.) [3 points]
(1) $2 \cdot 3 ^ { \frac { 1 } { 3 } }$
(2) $2 \cdot 3 ^ { \frac { 2 } { 3 } }$
(3) $2 ^ { \frac { 1 } { 2 } } \cdot 3 ^ { \frac { 1 } { 3 } }$
(4) $3 \cdot 2 ^ { \frac { 1 } { 3 } }$
(5) $3 \cdot 2 ^ { \frac { 2 } { 3 } }$

What is the value of $9 ^ { \frac { 3 } { 2 } } \times 27 ^ { - \frac { 2 } { 3 } }$? [2 points]
(1) $\frac { 1 } { 3 }$
(2) 1
(3) $\sqrt { 3 }$
(4) 3
(5) $3 \sqrt { 3 }$

What is the value of $9 ^ { \frac { 3 } { 2 } } \times 27 ^ { - \frac { 2 } { 3 } }$? [2 points]
(1) $\frac { 1 } { 3 }$
(2) 1
(3) $\sqrt { 3 }$
(4) 3
(5) $3 \sqrt { 3 }$

What is the value of $27 ^ { \frac { 1 } { 3 } } + \log _ { 2 } 4$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

What is the value of $27 ^ { \frac { 1 } { 3 } } + \log _ { 2 } 4$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

What is the value of $8 ^ { \frac { 2 } { 3 } } \times 9 ^ { \frac { 1 } { 2 } }$? [2 points]
(1) 4
(2) 6
(3) 8
(4) 10
(5) 12

What is the value of $5 \times 8 ^ { \frac { 1 } { 3 } }$? [2 points]
(1) 10
(2) 15
(3) 20
(4) 25
(5) 30

What is the value of $8 ^ { \frac { 1 } { 3 } } + 27 ^ { \frac { 2 } { 3 } }$? [2 points]
(1) 8
(2) 9
(3) 10
(4) 11
(5) 12

What is the value of $8 \times 2 ^ { - 2 }$? [2 points]
(1) 1
(2) 2
(3) 4
(4) 8
(5) 16

Find the value of $2 \times 16 ^ { \frac { 1 } { 4 } }$. [2 points]
(1) 2
(2) 4
(3) 6
(4) 8
(5) 10

What is the value of $2 ^ { - 1 } \times 16 ^ { \frac { 1 } { 2 } }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

What is the value of $16 \times 2 ^ { - 3 }$? [2 points]
(1) 1
(2) 2
(3) 4
(4) 8
(5) 16

What is the value of $3 ^ { 0 } \times 8 ^ { \frac { 2 } { 3 } }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

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

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

What is the value of $\left( \frac { 4 } { 2 ^ { \sqrt { 2 } } } \right) ^ { 2 + \sqrt { 2 } }$? [2 points]
(1) $\frac { 1 } { 4 }$
(2) $\frac { 1 } { 2 }$
(3) 1
(4) 2
(5) 4

Find the value of $\sqrt[3]{24} \times 3^{\frac{2}{3}}$. [2 points]
(1) 6
(2) 7
(3) 8
(4) 9
(5) 10

What is the value of $\sqrt[3]{5} \times 25^{\frac{1}{3}}$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5