Rooting a Tower

Algebra Level 3

What is the square root of

$\Large 4 ^ { 3 ^ 2 }?$

2 ^ 3

\large 2 ^ { 3 ^2 }

4 ^ 3

\large 2 ^ { 3 ^ 4 }

1 solution

Brian Charlesworth
Jan 27, 2017

$\Large (4^{3^{2}})^{\frac{1}{2}} = 4^{3^{2} \times \frac{1}{2}} = 4^{\frac{1}{2} \times 3^{2}} = (4^{\frac{1}{2}})^{3^{2}} = \boxed{2^{3^{2}}} = 2^{9}$ .

Compare to the other options given of $\Large 2^{3}, 4^{3} = 2^{6}$ and $\Large 2^{3^{4}} = 2^{81}$ .

Thanks for the solution, which others can learn from. You have clearly expressed the idea I was going for, which is that the (square) root is "applied to the base", which allows us to simplify the exponent.

I am slightly dismayed at the low correct rate.

Calvin Lin Staff - 4 years, 4 months ago

Yes, this issue keeps coming up, and when I saw the low correct rate I felt the need to write as clear a step-by-step solution as possible.

Brian Charlesworth - 4 years, 4 months ago

Rooting a Tower

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