Difference between revisions of "1970 AHSME Problems/Problem 13"

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[[Category: Introductory Algebra Problems]]
 
[[Category: Introductory Algebra Problems]]
 
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Revision as of 15:40, 2 October 2014

Problem

Given the binary operation $\star$ defined by $a\star b=a^b$ for all positive numbers $a$ and $b$. Then for all positive $a,b,c,n$, we have

$\text{(A) } a\star b=b\star a\quad\qquad\qquad\ \text{(B) } a\star (b\star c)=(a\star b) \star c\quad\\ \text{(C) } (a\star b^n)=(a \star n) \star b\quad \text{(D) } (a\star b)^n =a\star (bn)\quad\\ \text{(E) None of these}$

Solution

$\fbox{D}$

See also

1970 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
All AHSME Problems and Solutions

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