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Difference between revisions of "1956 AHSME Problems/Problem 9"

(Created page with "== Solution == Notice that the first part and the second part of the expression are the same things, just in a different order, ie 3 and the 6 are switched around. Therefore,...")
 
 
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== Problem 9==
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When you simplify <math>\left[ \sqrt [3]{\sqrt [6]{a^9}} \right]^4\left[ \sqrt [6]{\sqrt [3]{a^9}} \right]^4</math>, the result is:
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<math>\textbf{(A)}\ a^{16} \qquad\textbf{(B)}\ a^{12} \qquad\textbf{(C)}\ a^8 \qquad\textbf{(D)}\ a^4 \qquad\textbf{(E)}\ a^2 </math>
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== Solution ==
 
== Solution ==
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This simplifies to
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<cmath>(a^{\frac{9}{6}/3})^4 \cdot (a^{\frac{9}{3}/6})^4 = (a^{\frac{1}{2}})^4 \cdot (a^{\frac{1}{2}})^4 = (a^2)(a^2) = \boxed{a^4}</cmath>
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The answer is <math>\boxed{\textbf{(D)}}.</math>
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==See Also==
  
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Notice that the first part and the second part of the expression are the same things, just in a different order, ie 3 and the 6 are switched around.
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{{AHSME box|year=1956|num-b=8|num-a=10}}
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Therefore, the question is reduced to
 
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<cmath>2 \cdot [root{3}{root{6}{a^{9}}}]</cmath>
 
  
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Therefore, the answer is <math>\fbox{(A) 10}</math>
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[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 21:29, 12 February 2021

Problem 9

When you simplify $\left[ \sqrt [3]{\sqrt [6]{a^9}} \right]^4\left[ \sqrt [6]{\sqrt [3]{a^9}} \right]^4$, the result is:

$\textbf{(A)}\ a^{16} \qquad\textbf{(B)}\ a^{12} \qquad\textbf{(C)}\ a^8 \qquad\textbf{(D)}\ a^4 \qquad\textbf{(E)}\ a^2$

Solution

This simplifies to \[(a^{\frac{9}{6}/3})^4 \cdot (a^{\frac{9}{3}/6})^4 = (a^{\frac{1}{2}})^4 \cdot (a^{\frac{1}{2}})^4 = (a^2)(a^2) = \boxed{a^4}\] The answer is $\boxed{\textbf{(D)}}.$

See Also

1956 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
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
All AHSME Problems and Solutions

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