Question

calculeaza:(2 la puterea 37:2 la puterea 10+6 la puterea 23:6 la puterea 13):[2 la puterea 10×3 la puterea 10+(2 la puterea 14) la puterea 2]

Answer 1

$( {2}^{37} \div {2}^{10} + {6}^{23} \div {6}^{13} ) \div [ {2}^{10} \times {3}^{10} + {( {2}^{14}) }^{2} ]$

$= ( {2}^{37 - 10} + {6}^{23 - 13} ) \div [ {(2 \times 3)}^{10} + {2}^{14 \times 2} ]$

$= ( {2}^{27} + {6}^{10} ) \div ( {6}^{10} + {2}^{28} )$

$= ( {2}^{27} + {6}^{10} ) \div ( {2}^{28} + {6}^{10} )$

$= {2}^{27} \div {2}^{28} + {6}^{10} \div {6}^{10}$

$= {2}^{27 - 28} + 1$

$= {2}^{ - 1} + 1$

$= \frac{1}{2} + 1$

$= \frac{1}{2} + \frac{2}{2}$

$= \frac{1 + 2}{2}$

$= \frac{3}{2}$