Question

E3. Să se calculeze: 1 1 3 92; 49 2; 644; 2 ()¹ (19) 8 3 16 27 49 -1.5 3 (0,008)³; (2,25)³²;√√(0,027) ².​


Dau coroană

Answer 1

Explicație pas cu pas:

${9}^{ \frac{1}{2} } = \sqrt{9} = \sqrt{ {3}^{2} } = \bf 3$

${49}^{ - \frac{1}{2} } = \frac{1}{ \sqrt{49} } = \frac{1}{ \sqrt{ {7}^{2} } } = \bf \frac{1}{7}$

${64}^{ \frac{3}{4} } = {( {2}^{6} )}^{ \frac{3}{4} } = {2}^{ \frac{9}{2} } = \sqrt{ {2}^{9} } = {2}^{4} \sqrt{2} = \bf 16 \sqrt{2}$

${\Big( \frac{8}{27} \Big)}^{ - \frac{2}{3} } = {\Big( \frac{27}{8} \Big)}{\frac{2}{3} } = {\Big( \frac{ {3}^{3} }{ {2}^{3} } \Big)}^{\frac{2}{3} } = {\Big( \frac{3}{2} \Big)}^{3 \cdot \frac{2}{3} } = {\Big( \frac{3}{2} \Big)}^{2} = \bf \frac{9}{4}$

${\Big( \frac{16}{49} \Big)}^{-1.5} = {{\Big( \frac{49}{16} \Big)}}^{ \frac{3}{2} } = {\Big( \frac{ {7}^{2} }{ {4}^{2} } \Big)}^{\frac{3}{2} } = {\Big( \frac{7}{4} \Big)}^{2 \cdot \frac{3}{2} } = {\Big( \frac{7}{4} \Big)}^{3} = \bf \frac{343}{64}$

${(0.008)}^{ \frac{2}{3} } = {\Big( \frac{8}{1000} \Big)}^{ \frac{2}{3} } = {\Big( \frac{ {2}^{3} }{ {10}^{3} } \Big)}^{ \frac{2}{3} } = {\Big( \frac{2}{10} \Big)}^{3 \cdot \frac{2}{3} } = {\Big( \frac{1}{5} \Big)}^{2} = \bf \frac{1}{25}$

${(2,25)}^{ - \frac{3}{2} } = {\Big( \frac{225}{100} \Big)}^{ - \frac{3}{2} } = {\Big( \frac{100}{225} \Big)}^{ \frac{3}{2} } = {\Big( \frac{ {10}^{2} }{ {15}^{2} } \Big)}^{ \frac{3}{2} } = {\Big( \frac{10^{(5} }{15} \Big)}^{2 \cdot \frac{3}{2} } = {\Big( \frac{2}{3} \Big)}^{3} = \bf \frac{8}{27}$

$\sqrt[3]{ {(0.027)}^{ - 2} } = \sqrt[3]{{\Big( \frac{27}{1000} \Big)}^{ - 2}} = \sqrt[3]{{\Big( \frac{ {10}^{3} }{ {3}^{3} } \Big)}^{2}} = \sqrt[3]{{\Big( \frac{10}{3} \Big)}^{3 \cdot 2}} = \sqrt[3]{{\Big( \frac{10}{3} \Big)}^{6}} = {\Big( \frac{10}{3} \Big)}^{ \frac{6}{3} } = {\Big( \frac{10}{3} \Big)}^{2} = \frac{100}{9} = 11 \frac{1}{9} = 11.(1)$