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 (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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