Question

Упростить выражения .​

Answer 1

Пошаговое объяснение:

$1) {2}^{ - 1} \times {64}^{ \frac{2}{3} } = {2}^{ - 1} \times {2}^{4} = {2}^{ - 1 + 4} = {2}^{3} = 8$

$2) {3}^{ - 2} \times {81}^{ \frac{1}{4} } = {3}^{ - 2} ( {3}^{4} )^{ \frac{1}{4} } = ( {3}^{4} )^{ \frac{1}{4} } = {3}^{ - 2} \times 3 = {3}^{ - 1} = \frac{1}{3}$

$3) {100}^{ - \frac{1}{2} } = \frac{1}{ {100}^{ { \frac{1}{2} }^{} } } = \frac{1}{( {10}^{2})^{ \frac{1}{2} } } = {10}^{2 \times \frac{1}{2} } = {10}^{1} = \frac{1}{10}$

$4) {(27 \times 125)}^{ \frac{1}{3} } = {3375}^{ \frac{1}{3} } = ( {15}^{3} )^{ \frac{1}{3} } = {15^{1} } = 15$

$5)( \frac{1}{36} \times 0.04)^{ \frac{1}{2} } = ( \frac{1}{36} \times \frac{1}{25} ) ^{2 \frac{1}{2} } = \frac{1}{36 \times 25} = ( \frac{1}{900} )^{ \frac{1}{2} } = \sqrt{ \frac{1}{900} } = \frac{1}{30}$

$6)( \frac{1}{16} \times {81}^{ - 2})^{ - \frac{1}{4} } = ( \frac{1}{16} \times \frac{1}{ {81}^{2} } )^{ - \frac{1}{4} } = ( \frac{1}{ {16 \times 81}^{2} } ) ^{ - \frac{1}{4} } = ( {16 \times 81}^{2} )^{ \frac{1}{4} } = \sqrt[4]{ {16 \times 81}^{2} } = \sqrt[4]{ {324}^{2} } = \sqrt{324} = 18$