Question

Cum se rezolva 8 la puterea -1/2?
Multumesc

Answer 1

Răspuns:

$\mathbf{ \frac{ \sqrt{2} }{4} }$

Explicație pas cu pas:

$\mathbf{8 {}^{ - \frac{1}{2} } = \frac{1}{8 {}^{ \frac{1}{2} } }; a {}^{ - n } = \frac{1}{a {}^{n} } }$

$\mathbf{ = \frac{1}{ \sqrt{8} } \: am \: transformat \: folosind \: a {}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } }$

$\mathbf{ = \frac{1}{2 \sqrt{2} } = \frac{1}{2 \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{1 \sqrt{2} }{2 \sqrt{2} \sqrt{2} } }$

$\mathbf{ \frac{ \sqrt{2} }{2 \times 2} =\boxed{\mathbf{ \frac{ \sqrt{2} }{4} }}}$

Bafta ! :)

Answer 2

$\it 8^{-\frac{1}{2}}=\dfrac{1}{8^{\frac{1}{2}}}=\dfrac{^{\sqrt8)}1}{\sqrt8}=\dfrac{\sqrt8}{8}=\dfrac{\sqrt{4\cdot2}}{8}=\dfrac{\ 2\sqrt2^{(2}}{8}=\dfrac{\sqrt2}{4}$