LFM Pure and Mechanics

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brazil-enem 2012 Q168 Evaluating Expressions Using Index Laws View
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
Many physiological and biochemical processes, such as heartbeats and respiration rate, present scales constructed from the relationship between surface area and mass (or volume) of the animal. One of these scales, for example, considers that ``the cube of the surface area $S$ of a mammal is proportional to the square of its mass $M$''.
This is equivalent to saying that, for a constant $k > 0$, the area $S$ can be written as a function of $M$ by means of the expression:
(A) $S = k \cdot M$ (B) $S = k \cdot M^{\frac{1}{3}}$ (C) $S = k^{\frac{1}{3}} \cdot M^{\frac{1}{3}}$ (D) $S = k^{\frac{1}{3}} \cdot M^{\frac{2}{3}}$ (E) $S = k^{\frac{1}{3}} \cdot M^{2}$
brazil-enem 2015 Q170 Evaluating Expressions Using Index Laws View
QUESTION 170
The value of $2^{10}$ is
(A) 512
(B) 1024
(C) 2048
(D) 4096
(E) 8192
brazil-enem 2015 Q175 Simplifying Surd Expressions View
QUESTION 175
The value of $\sqrt{144} + \sqrt{25}$ is
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
brazil-enem 2024 Q177 Evaluating Expressions Using Index Laws View
The value of $2^{10}$ is:
(A) 512
(B) 1024
(C) 2048
(D) 4096
(E) 8192
csat-suneung 2005 Q1 2 marks Evaluating Expressions Using Index Laws View
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
csat-suneung 2005 Q1 2 marks Evaluating Expressions Using Index Laws View
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
csat-suneung 2006 Q1 2 marks Evaluating Expressions Using Index Laws View
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
csat-suneung 2006 Q1 2 marks Evaluating Expressions Using Index Laws View
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
csat-suneung 2008 Q1 2 marks Simplify or Evaluate a Logarithmic Expression View
What is the value of $8 ^ { \frac { 2 } { 3 } } + \log _ { 2 } 8$? [2 points]
(1) 5
(2) 6
(3) 7
(4) 8
(5) 9
csat-suneung 2008 Q1 2 marks Simplify or Evaluate a Logarithmic Expression View
The value of $8 ^ { \frac { 2 } { 3 } } + \log _ { 2 } 8$ is? [2 points]
(1) 5
(2) 6
(3) 7
(4) 8
(5) 9
csat-suneung 2008 Q4 3 marks Evaluating Expressions Using Index Laws View
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) $3 \cdot 2 ^ { \frac { 2 } { 3 } }$
csat-suneung 2009 Q1 2 marks Evaluating Expressions Using Index Laws View
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) $3 \sqrt { 3 }$
csat-suneung 2009 Q1 2 marks Evaluating Expressions Using Index Laws View
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) $3 \sqrt { 3 }$
csat-suneung 2010 Q1 2 marks Evaluating Expressions Using Index Laws View
What is the value of $27 ^ { \frac { 1 } { 3 } } + \log _ { 2 } 4$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
csat-suneung 2013 Q26 4 marks Number-Theoretic Reasoning with Indices View
For natural numbers $n$ with $2 \leq n \leq 100$, find the number of values of $n$ such that $\left( \sqrt[3]{3^5} \right)^{\frac{1}{2}}$ is the $n$-th root of some natural number. [4 points]
csat-suneung 2014 Q1 2 marks Evaluating Expressions Using Index Laws View
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
csat-suneung 2015 Q1 2 marks Evaluating Expressions Using Index Laws View
What is the value of $5 \times 8 ^ { \frac { 1 } { 3 } }$? [2 points]
(1) 10
(2) 15
(3) 20
(4) 25
(5) 30
csat-suneung 2016 Q3 2 marks Evaluating Expressions Using Index Laws View
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
csat-suneung 2017 Q1 2 marks Evaluating Expressions Using Index Laws View
What is the value of $8 \times 2 ^ { - 2 }$? [2 points]
(1) 1
(2) 2
(3) 4
(4) 8
(5) 16
csat-suneung 2018 Q1 2 marks Evaluating Expressions Using Index Laws View
Find the value of $2 \times 16 ^ { \frac { 1 } { 4 } }$. [2 points]
(1) 2
(2) 4
(3) 6
(4) 8
(5) 10
csat-suneung 2019 Q1 2 marks Evaluating Expressions Using Index Laws View
What is the value of $2 ^ { - 1 } \times 16 ^ { \frac { 1 } { 2 } }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
csat-suneung 2020 Q1 2 marks Evaluating Expressions Using Index Laws View
What is the value of $16 \times 2 ^ { - 3 }$? [2 points]
(1) 1
(2) 2
(3) 4
(4) 8
(5) 16
csat-suneung 2021 Q1 2 marks Evaluating Expressions Using Index Laws View
What is the value of $3 ^ { 0 } \times 8 ^ { \frac { 2 } { 3 } }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
csat-suneung 2021 Q1 2 marks Evaluating Expressions Using Index Laws View
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