Question

Resolva a potenciação com raiz: ⁴√2³⁶+2³⁴/20

Answer 1

$\sqrt[4]{ {2}^{36} } + \frac{ {2}^{34} }{20} = \\ \sqrt[4]{ {2}^{4} \times {2}^{4} \times {2}^{4} \times {2}^{4} \times {2}^{4} \times {2}^{4} \times {2}^{4} \times {2}^{4} \times {2}^{4}} + \frac{ {2}^{34} }{20} \\ 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 + \frac{ {2}^{34} }{20} = \\ 512 + \frac{ {2}^{34} }{20} = \\ {2}^{8} + \frac{ {2}^{34} }{20} =$

Answer 2

Lembrando que:

$\rightarrow~\sqrt[b]{a^c}~=~a^{\frac{c}{b}}$

$\sqrt[4]{\frac{2^{36}+2^{34}}{20}}\\\\\\\sqrt[4]{\frac{2^{34}(2^2+1)}{5~.~2^2}}\\\\\\\sqrt[4]{\frac{2^{34}~.~5}{5~.~2^2}}\\\\\\\sqrt[4]{2^{34-2}~.~5^{1-1}}\\\\\\\sqrt[4]{2^{32}~.~1}\\\\\\2^{\frac{32}{4}}\\\\\\2^8\\\\\\\boxed{256}$