Difference between revisions of "1956 AHSME Problems/Problem 9"
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| + | == Problem 9== | ||
| + | |||
| + | 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: | ||
| + | |||
| + | <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> | ||
| + | |||
== Solution == | == Solution == | ||
| + | This simplifies to | ||
| + | <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> | ||
| + | The answer is <math>\boxed{\textbf{(D)}}.</math> | ||
| + | ==See Also== | ||
| − | + | {{AHSME box|year=1956|num-b=8|num-a=10}} | |
| − | |||
| − | |||
| − | + | [[Category:Introductory Algebra Problems]] | |
| + | {{MAA Notice}} | ||
Latest revision as of 20:29, 12 February 2021
Problem 9
When you simplify ![$\left[ \sqrt [3]{\sqrt [6]{a^9}} \right]^4\left[ \sqrt [6]{\sqrt [3]{a^9}} \right]^4$](http://latex.artofproblemsolving.com/5/8/4/58445c91c8f5fb52978a56369a3c2e6d48dcd1b8.png)
, the result is:
Solution
This simplifies to
![\[(a^{\frac{9}{6}/3})^4 \cdot (a^{\frac{9}{3}/6})^4 = (a^{\frac{1}{2}})^4 \cdot (a^{\frac{1}{2}})^4 = (a^2)(a^2) = \boxed{a^4}\]](http://latex.artofproblemsolving.com/2/0/3/203b6f8ba129e737d1542bd14f877189ba474876.png)
The answer is 
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
