# 1979 AHSME Problems/Problem 9

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## Problem 9

The product of $\sqrt[3]{4}$ and $\sqrt[4]{8}$ equals

$\textbf{(A) }\sqrt[7]{12}\qquad \textbf{(B) }2\sqrt[7]{12}\qquad \textbf{(C) }\sqrt[7]{32}\qquad \textbf{(D) }\sqrt[12]{32}\qquad \textbf{(E) }2\sqrt[12]{32}$

## Solution

Solution by e_power_pi_times_i

$\sqrt[3]{4}$ and $\sqrt[4]{8}$ can be expressed as $2^{\frac{2}{3}}$ and $2^{\frac{3}{4}}$, so their product is $2^{\frac{17}{12}} = \boxed{\textbf{(E) } 2\sqrt[12]{32}}$.

## See also

 1979 AHSME (Problems • Answer Key • Resources) Preceded byProblem 8 Followed byProblem 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.

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