Question

50 de puncte.
Sa se scrie ca putere cu exponent rational
√2√2√2
Explicatie va rog

Answer 1

Stim ca $\sqrt{a}= a^{ \frac{1}{2} }$.

$\sqrt{2 \sqrt{2 \sqrt{2} } }= \sqrt{2 \sqrt{2* 2^{1/2} } } = \sqrt{2 \sqrt{2 ^{3/2} } } = \sqrt{2*(2 ^{3/2}) ^{1/2} }=$$\sqrt{2* 2^{3/4} }= \sqrt{2 ^{7/4} } = (2^{7/4})^{1/2}= 2^{ \frac{7}{8} }$