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Difference between revisions of "2013 CEMC Gauss (Grade 8) Problems/Problem 12"

(Created page with "== Problem == The value of <math>(2^3)^2 - 4^3</math> is <math> \textbf{(A)}\ 0 \qquad \textbf{(B)}\ -8 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 10 \qquad \textbf{(E)}\ 12...")
 
 
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~anabel.disher
 
~anabel.disher
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{{CEMC box|year=2013|competition=Gauss (Grade 8)|num-b=11|num-a=13}}

Latest revision as of 21:47, 18 October 2025

Problem

The value of $(2^3)^2 - 4^3$ is

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ -8 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 10 \qquad \textbf{(E)}\ 12$

Solution 1

$(2^3)^2 - 4^3 = 8^2 - 4^3 = 64 - 64 = \boxed {\textbf {(A) } 0}$

~anabel.disher

Solution 2

We can notice that $(a^x)^y = a^{xy} = (a^y)^x$, and use the fact that $a - a = 0$ to get the answer:

$(2^3)^2 - 4^3 = (2^2)^3 - 4^3 = 4^3 - 4^3 = \boxed {\textbf {(A) } 0}$

~anabel.disher

Solution 3

$(2^3)^2 - 4^3 = 2^{3 \times 2} - 4^3 = 2^6 - 4^3 = 64 - 64 = \boxed {\textbf {(A) } 0}$

~anabel.disher

2013 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources)
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CEMC Gauss (Grade 8)
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