Question

valoarea expresiei $(\frac{1}{2} )^{13} *4^{\frac{\sqrt{3} }{2} } *(\frac{1}{8} )^{\sqrt{27} } *16^{3}$ este
A (mai mare decat 1) B (mai mica decat 1) C(egal cu 1)

Answer 1

$\left(\frac{1}{2}\right)^{13} \cdot 4^{\frac{\sqrt{3} }{2} }\cdot \left(\frac{1}{8} \right)^{\sqrt{27} } \cdot 16^{3} = \\ = {2}^{ - 13} \cdot {2}^{2 \cdot \frac{ \sqrt{3} }{2} }\cdot {2}^{ - 3 \cdot \sqrt{27} }\cdot {2}^{4 \cdot 3} = \\ = {2}^{ - 13 + \sqrt{3} - 3 \cdot 3 \sqrt{ 3} + 12 } = \\ = {2}^{ - 1 - 8 \sqrt{3} } =\\ = \frac{1}{2^{ 1 +8 \sqrt{3} }}< 1$

B) corect.