Question

Zapisz liczbę w postaci potęgi o podstawie 2:
[tex]\sqrt{32} * \sqrt[7]{8\sqrt[11]{16\sqrt{2} } }[/tex]

Answer 1

Odpowiedź:

[tex]\sqrt{32} * \sqrt[7]{8\sqrt[11]{16\sqrt{2}}} = \sqrt{2^{5}} * \sqrt[7]{2^{3}\sqrt[11]{2^{4}\sqrt{2}}} = 2^{\frac{5}{2}} * \sqrt[7]{2^{3}\sqrt[11]{2^{4}*2^{\frac{1}{2}}}} = 2^{\frac{5}{2}} * \sqrt[7]{2^{3} * 2^{\frac{2}{11}}} =[/tex]

[tex]= 2^{\frac{5}{2}} * 2^{\frac{6}{77}} = 2^{\frac{30}{154}} = 2^{\frac{15}{77}}[/tex]